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Analytic structure of the QCD phase diagram in the complex-temperature plane
Authors:
Gokce Basar,
Vladimir V. Skokov
Abstract:
We study the analytic structure of the QCD phase diagram by treating temperature as a complex variable. The nearest Yang-Lee edge singularities in the complex $T$ plane bound the domain of analyticity of temperature-dependent thermodynamic observables and complement the more commonly studied singularities in the complex chemical-potential plane. Our analysis combines three complementary perspectiv…
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We study the analytic structure of the QCD phase diagram by treating temperature as a complex variable. The nearest Yang-Lee edge singularities in the complex $T$ plane bound the domain of analyticity of temperature-dependent thermodynamic observables and complement the more commonly studied singularities in the complex chemical-potential plane. Our analysis combines three complementary perspectives: universal critical scaling, a first-principles extraction from lattice-QCD data, and explicit illustrations in effective models. We illustrate the resulting structure in a random-matrix model and in a quark-meson model, where the singularity trajectories can be followed explicitly. At small real chemical potential, the leading complex-temperature singularity admits an analytic expansion in $μ^2$, while near a critical point it crosses over to the universal Puiseux form dictated by Ising critical scaling. We show that the complex-$T$ and complex-$μ$ trajectories are controlled by the same scaling variables and mapping coefficients, so their comparison provides a stringent consistency test of critical-point searches and constrains the extent of the critical scaling regime. Finally, we analyze lattice-QCD data at $μ=0$ using an iterated conformal-Pade approach and extract the continuum location of the nearest complex-temperature singularity. The result is consistent with the expectation that, at physical quark masses, the real part of the leading singularity lies between the chiral-limit transition temperature and the physical-mass chiral-susceptibility peak temperature, while its imaginary part remains nonzero.
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Submitted 10 June, 2026;
originally announced June 2026.
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Non-Gaussian hydrodynamic fluctuations in an expanding relativistic fluid
Authors:
Gokce Basar,
Shuo Song
Abstract:
We consider non-equilibrium evolution of non-Gaussian fluctuations in a hydrodynamic system undergoing a boost-invariant expansion described by Bjorken flow. We derive the evolution equations for two- and three-point velocity correlators using the effective field theory framework and present analytical solutions for them. We show that the average Landau frame is better suited for studying non-Gaus…
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We consider non-equilibrium evolution of non-Gaussian fluctuations in a hydrodynamic system undergoing a boost-invariant expansion described by Bjorken flow. We derive the evolution equations for two- and three-point velocity correlators using the effective field theory framework and present analytical solutions for them. We show that the average Landau frame is better suited for studying non-Gaussian fluctuations of velocity when relativistic effects are important. In the Bjorken background, the average Landau frame corresponds to the density frame. We demonstrate that the three-point correlators depend nonlinearly on the non-equilibrium dynamics of the two-point functions, and exhibit non-trivial effects such as memory. The importance of these effects in the context of the search for the QCD critical point via fluctuations is discussed.
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Submitted 30 April, 2026;
originally announced April 2026.
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Non-Gaussian fluctuations in relativistic hydrodynamics: Confluent equations for three-point correlations
Authors:
Xin An,
Gokce Basar,
Mikhail Stephanov
Abstract:
We derive deterministic equations for the evolution of non-Gaussian fluctuations in relativistic stochastic hydrodynamics. This is achieved by defining the average local Landau frame and corresponding fluctuating hydrodynamic variables. Fully nonlinear stochastic hydrodynamics is expressed in a unified multi-component matrix form. A novel relativistic formalism, also manifestly covariant under SO(…
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We derive deterministic equations for the evolution of non-Gaussian fluctuations in relativistic stochastic hydrodynamics. This is achieved by defining the average local Landau frame and corresponding fluctuating hydrodynamic variables. Fully nonlinear stochastic hydrodynamics is expressed in a unified multi-component matrix form. A novel relativistic formalism, also manifestly covariant under SO(3) rotations of the local spatial basis in the average local Landau frame, is introduced. The equations describe correlators of all hydrodynamic variables, including fluctuating velocity (or momentum density) -- a nontrivial problem in relativistic hydrodynamics.
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Submitted 15 April, 2026;
originally announced April 2026.
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Equation of state and cumulants of proton multiplicity in equilibrium near critical point from Pade estimates
Authors:
Gokce Basar,
Maneesha Pradeep,
Mikhail Stephanov
Abstract:
The fluctuations of proton multiplicity in heavy-ion collisions are the key observables in the search for the QCD critical point. In this work we present an approach to constraining the cumulants of proton number based on the analytical properties of the QCD equation of state in the vicinity of the critical point. We show that, under the assumption of local equilibrium, the features of the collisi…
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The fluctuations of proton multiplicity in heavy-ion collisions are the key observables in the search for the QCD critical point. In this work we present an approach to constraining the cumulants of proton number based on the analytical properties of the QCD equation of state in the vicinity of the critical point. We show that, under the assumption of local equilibrium, the features of the collision energy dependence, such as the peaks and the dips of the cumulants, are significantly constrained by the data on the Lee-Yang singularity structure available via Pade resummation of the lattice QCD data. Furthermore, we identify four topologically distinct scenarios, all within the uncertainty range of the Pade estimates for the non-universal mapping parameters, classified based on the location of the critical point and the slope of the chiral crossover curve with respect to the freeze-out curve. These different scenarios result in qualitatively different critical signatures, especially for the third factorial cumulant and thus could be potentially discriminated using the experimental data.
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Submitted 24 March, 2026;
originally announced March 2026.
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Recent developments in relativistic hydrodynamic fluctuations
Authors:
Gokce Basar
Abstract:
The study of thermal fluctuations in relativistic hydrodynamics has led to numerous important developments in the last decade. We present a bird's eye view of the recent advances on the theory of fluctuations on three fronts; stochastic hydrodynamics, hydro-kinetics where fluctuations are included as additional modes that satisfy deterministic evolution equations, and effective field theory formul…
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The study of thermal fluctuations in relativistic hydrodynamics has led to numerous important developments in the last decade. We present a bird's eye view of the recent advances on the theory of fluctuations on three fronts; stochastic hydrodynamics, hydro-kinetics where fluctuations are included as additional modes that satisfy deterministic evolution equations, and effective field theory formulation of relativistic hydrodynamics. We compare and contrast these different but complimentary frameworks and highlight various recent progresses in each of them.
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Submitted 3 October, 2024;
originally announced October 2024.
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Hyperfine Structure Investigation of Singly Ionized Thulium in FT Spectra
Authors:
T. Y. Kebapci,
S. Parlatan,
S. Sert,
I. K. Ozturk,
G. Basar,
T. Sahin,
S. Bilir,
R. Ferber,
M. Tamanis,
S. Kroger
Abstract:
The hyperfine structure of 40 spectral lines of singly ionized thulium (Tm II) in emission spectra from a hollow cathode discharge lamp measured with a Fourier transform spectrometer in the wavelength range from 335 nm to 2345 nm has been investigated. As a result of the analysis, the magnetic dipole hyperfine structure constants $A$ for 27 fine structure levels of Tm II were determined for the fi…
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The hyperfine structure of 40 spectral lines of singly ionized thulium (Tm II) in emission spectra from a hollow cathode discharge lamp measured with a Fourier transform spectrometer in the wavelength range from 335 nm to 2345 nm has been investigated. As a result of the analysis, the magnetic dipole hyperfine structure constants $A$ for 27 fine structure levels of Tm II were determined for the first time. In addition, the values of two magnetic dipole hyperfine structure constants $A$ from the literature were declared incorrect and the corrected values were given.
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Submitted 8 May, 2024;
originally announced May 2024.
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The stochastic relativistic advection diffusion equation from the Metropolis algorithm
Authors:
Gokce Basar,
Jay Bhambure,
Rajeev Singh,
Derek Teaney
Abstract:
We study an approach to simulating the stochastic relativistic advection-diffusion equation based on the Metropolis algorithm. We show that the dissipative dynamics of the boosted fluctuating fluid can be simulated by making random transfers of charge between fluid cells, interspersed with ideal hydrodynamic time steps. The random charge transfers are accepted or rejected in a Metropolis step usin…
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We study an approach to simulating the stochastic relativistic advection-diffusion equation based on the Metropolis algorithm. We show that the dissipative dynamics of the boosted fluctuating fluid can be simulated by making random transfers of charge between fluid cells, interspersed with ideal hydrodynamic time steps. The random charge transfers are accepted or rejected in a Metropolis step using the entropy as a statistical weight. This procedure reproduces the expected strains of dissipative relativistic hydrodynamics in a specific (and non-covariant) hydrodynamic frame known as the density frame. Numerical results, both with and without noise, are presented and compared to relativistic kinetics and analytical expectations. An all order resummation of the density frame gradient expansion reproduces the covariant dynamics in a specific model. In contrast to all other numerical approaches to relativistic dissipative fluids, the dissipative fluid formalism presented here is strictly first order in gradients and has no non-hydrodynamic modes. The physical naturalness and simplicity of the Metropolis algorithm, together with its convergence properties, make it a promising tool for simulating stochastic relativistic fluids in heavy ion collisions and for critical phenomena in the relativistic domain.
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Submitted 27 July, 2024; v1 submitted 6 March, 2024;
originally announced March 2024.
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Relativistic fluctuations in stochastic fluid dynamics
Authors:
Xin An,
Gokce Basar,
Mikhail Stephanov,
Ho-Ung Yee
Abstract:
The state-of-the-art theoretical formalism for a covariant description of non-Gaussian fluctuation dynamics in relativistic fluids is discussed.
The state-of-the-art theoretical formalism for a covariant description of non-Gaussian fluctuation dynamics in relativistic fluids is discussed.
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Submitted 28 February, 2024;
originally announced February 2024.
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On the QCD critical point, Lee-Yang edge singularities and Pade resummations
Authors:
Gokce Basar
Abstract:
We analyze the trajectory of the Lee-Yang edge singularities of the QCD equation of state in the complex baryon chemical potential ($μ_B$) plane for different values of the temperature by using the recent lattice results for the Taylor expansion coefficients up to eighth order in $μ_B$ and various resummation techniques that blend in Pade expansions and conformal maps. By extrapolating from this i…
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We analyze the trajectory of the Lee-Yang edge singularities of the QCD equation of state in the complex baryon chemical potential ($μ_B$) plane for different values of the temperature by using the recent lattice results for the Taylor expansion coefficients up to eighth order in $μ_B$ and various resummation techniques that blend in Pade expansions and conformal maps. By extrapolating from this information, we estimate for the location of the QCD critical point, $ T_c \approx 100$ MeV, $μ_c \approx 580$ MeV. We also estimate the crossover slope at the critical point to be $α_1 \approx 9^\circ$ and further constrain the non-universal mapping parameters between the three dimensional Ising model and QCD equations of state.
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Submitted 3 July, 2024; v1 submitted 11 December, 2023;
originally announced December 2023.
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Heavy-dense QCD, sign optimization and Lefschetz thimbles
Authors:
Gokce Basar,
Joseph Marincel
Abstract:
We study the heavy-dense limit of QCD on the lattice with heavy quarks at high density. The effective three dimensional theory has a sign problem which is alleviated by sign optimization where the path integration domain is deformed in complex space in a way that minimizes the phase oscillations. We simulate the theory via a Hybrid-Monte-Carlo, for different volumes, both to leading order and next…
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We study the heavy-dense limit of QCD on the lattice with heavy quarks at high density. The effective three dimensional theory has a sign problem which is alleviated by sign optimization where the path integration domain is deformed in complex space in a way that minimizes the phase oscillations. We simulate the theory via a Hybrid-Monte-Carlo, for different volumes, both to leading order and next-to-next-to leading order in the hopping expansion, and show that sign optimization successfully mitigates the sign problem at large enough volumes where usual re-weighting methods fail. Finally we show that there is a significant overlap between the complex manifold generated by sign optimization and the Lefschetz thimbles associated with the theory.
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Submitted 12 December, 2023; v1 submitted 10 November, 2023;
originally announced November 2023.
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Comparison of theory and experiment for radiative characteristics in neutral thulium
Authors:
Andrey I. Bondarev,
Maris Tamanis,
Ruvin Ferber,
Gönül Başar,
Sophie Kröger,
Mikhail G. Kozlov,
Stephan Fritzsche
Abstract:
Intensities in Tm I emission series originating from a common upper level are measured using a Fourier transform spectrometer. The derived relative transition probabilities within each series are compared to the theoretical predictions obtained from large-scale calculations that combine configuration interaction with many-body perturbation theory. Moreover, the Tm I spectrum recorded in an externa…
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Intensities in Tm I emission series originating from a common upper level are measured using a Fourier transform spectrometer. The derived relative transition probabilities within each series are compared to the theoretical predictions obtained from large-scale calculations that combine configuration interaction with many-body perturbation theory. Moreover, the Tm I spectrum recorded in an external magnetic field is analyzed. Our theoretical results well describe the current measurements and show no more than a two-fold difference from previous experimental data on absolute transition probabilities. Additionally, Landé g factors, hyperfine structure constants, and atomic electric quadrupole moments for several levels of interest are computed and compared to experimental observations, where available.
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Submitted 19 December, 2023; v1 submitted 13 October, 2023;
originally announced October 2023.
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The Present and Future of QCD
Authors:
P. Achenbach,
D. Adhikari,
A. Afanasev,
F. Afzal,
C. A. Aidala,
A. Al-bataineh,
D. K. Almaalol,
M. Amaryan,
D. Androić,
W. R. Armstrong,
M. Arratia,
J. Arrington,
A. Asaturyan,
E. C. Aschenauer,
H. Atac,
H. Avakian,
T. Averett,
C. Ayerbe Gayoso,
X. Bai,
K. N. Barish,
N. Barnea,
G. Basar,
M. Battaglieri,
A. A. Baty,
I. Bautista
, et al. (378 additional authors not shown)
Abstract:
This White Paper presents the community inputs and scientific conclusions from the Hot and Cold QCD Town Meeting that took place September 23-25, 2022 at MIT, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 424 physicists registered for the meeting. The meeting highlighted progress in Quantum Chromodynamics (QCD) nuclear physics since the 2015…
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This White Paper presents the community inputs and scientific conclusions from the Hot and Cold QCD Town Meeting that took place September 23-25, 2022 at MIT, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 424 physicists registered for the meeting. The meeting highlighted progress in Quantum Chromodynamics (QCD) nuclear physics since the 2015 LRP (LRP15) and identified key questions and plausible paths to obtaining answers to those questions, defining priorities for our research over the coming decade. In defining the priority of outstanding physics opportunities for the future, both prospects for the short (~ 5 years) and longer term (5-10 years and beyond) are identified together with the facilities, personnel and other resources needed to maximize the discovery potential and maintain United States leadership in QCD physics worldwide. This White Paper is organized as follows: In the Executive Summary, we detail the Recommendations and Initiatives that were presented and discussed at the Town Meeting, and their supporting rationales. Section 2 highlights major progress and accomplishments of the past seven years. It is followed, in Section 3, by an overview of the physics opportunities for the immediate future, and in relation with the next QCD frontier: the EIC. Section 4 provides an overview of the physics motivations and goals associated with the EIC. Section 5 is devoted to the workforce development and support of diversity, equity and inclusion. This is followed by a dedicated section on computing in Section 6. Section 7 describes the national need for nuclear data science and the relevance to QCD research.
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Submitted 4 March, 2023;
originally announced March 2023.
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Non-Gaussian fluctuation dynamics in relativistic fluids
Authors:
Xin An,
Gokce Basar,
Mikhail Stephanov,
Ho-Ung Yee
Abstract:
We consider non-equilibrium evolution of non-Gaussian fluctuations within relativistic hydrodynamics relevant for the QCD critical point search in heavy-ion collision experiments. We rely on the hierarchy of relaxation time scales, which emerges in the hydrodynamic regime near the critical point, to focus on the slowest mode such as the fluctuations of specific entropy, whose equilibrium magnitude…
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We consider non-equilibrium evolution of non-Gaussian fluctuations within relativistic hydrodynamics relevant for the QCD critical point search in heavy-ion collision experiments. We rely on the hierarchy of relaxation time scales, which emerges in the hydrodynamic regime near the critical point, to focus on the slowest mode such as the fluctuations of specific entropy, whose equilibrium magnitude, non-Gaussianity and typical relaxation time are increasing as the critical point is approached. We derive evolution equations for the non-Gaussian correlators of this diffusive mode in an arbitrary relativistic hydrodynamic flow. We compare with the simpler case of the stochastic diffusion on a static homogeneous background and identify terms which are specific to the case of the full hydrodynamics with pressure fluctuations and flow.
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Submitted 25 September, 2023; v1 submitted 28 December, 2022;
originally announced December 2022.
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Long Range Plan: Dense matter theory for heavy-ion collisions and neutron stars
Authors:
Alessandro Lovato,
Travis Dore,
Robert D. Pisarski,
Bjoern Schenke,
Katerina Chatziioannou,
Jocelyn S. Read,
Philippe Landry,
Pawel Danielewicz,
Dean Lee,
Scott Pratt,
Fabian Rennecke,
Hannah Elfner,
Veronica Dexheimer,
Rajesh Kumar,
Michael Strickland,
Johannes Jahan,
Claudia Ratti,
Volodymyr Vovchenko,
Mikhail Stephanov,
Dekrayat Almaalol,
Gordon Baym,
Mauricio Hippert,
Jacquelyn Noronha-Hostler,
Jorge Noronha,
Enrico Speranza
, et al. (39 additional authors not shown)
Abstract:
Since the release of the 2015 Long Range Plan in Nuclear Physics, major events have occurred that reshaped our understanding of quantum chromodynamics (QCD) and nuclear matter at large densities, in and out of equilibrium. The US nuclear community has an opportunity to capitalize on advances in astrophysical observations and nuclear experiments and engage in an interdisciplinary effort in the theo…
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Since the release of the 2015 Long Range Plan in Nuclear Physics, major events have occurred that reshaped our understanding of quantum chromodynamics (QCD) and nuclear matter at large densities, in and out of equilibrium. The US nuclear community has an opportunity to capitalize on advances in astrophysical observations and nuclear experiments and engage in an interdisciplinary effort in the theory of dense baryonic matter that connects low- and high-energy nuclear physics, astrophysics, gravitational waves physics, and data science
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Submitted 7 November, 2022; v1 submitted 3 November, 2022;
originally announced November 2022.
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QCD Phase Structure and Interactions at High Baryon Density: Continuation of BES Physics Program with CBM at FAIR
Authors:
D. Almaalol,
M. Hippert,
J. Noronha-Hostler,
J. Noronha,
E. Speranza,
G. Basar,
S. Bass,
D. Cebra,
V. Dexheimer,
D. Keane,
S. Radhakrishnan,
A. I. Sheikh,
M. Strickland,
C. Y. Tsang,
. X. Dong,
V. Koch,
G. Odyniec,
N. Xu,
F. Geurts,
D. Hofman,
M. Stephanov,
G. Wilks,
Z. Y. Ye,
H. Z. Huang,
G. Wang
, et al. (19 additional authors not shown)
Abstract:
We advocate for an active US participation in the international collaboration of the CBM experiment that will allow the US nuclear physics program to build on its successful exploration of the QCD phase diagram, use the expertise gained at RHIC to make complementary measurements at FAIR, and contribute to achieving the scientific goals of the beam energy scan (BES) program.
We advocate for an active US participation in the international collaboration of the CBM experiment that will allow the US nuclear physics program to build on its successful exploration of the QCD phase diagram, use the expertise gained at RHIC to make complementary measurements at FAIR, and contribute to achieving the scientific goals of the beam energy scan (BES) program.
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Submitted 21 December, 2022; v1 submitted 11 September, 2022;
originally announced September 2022.
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Sign optimization and complex saddle points in one-dimensional QCD
Authors:
Gokce Basar,
Joesph Marincel
Abstract:
We study one-dimensional QCD at finite quark density by using the sign optimization framework. The fermion sign problem is mitigated by deforming the path integral domain, $SU(3)$ to a complexified one ${\cal M} \subset SL(3)$, explicitly constructed to reduce the phase fluctuations. The complexification is constructed using the angular representation of $SU(3)$. We provide a physical explanation…
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We study one-dimensional QCD at finite quark density by using the sign optimization framework. The fermion sign problem is mitigated by deforming the path integral domain, $SU(3)$ to a complexified one ${\cal M} \subset SL(3)$, explicitly constructed to reduce the phase fluctuations. The complexification is constructed using the angular representation of $SU(3)$. We provide a physical explanation of the optimization procedure in terms of complex saddle points. This picture connects the sign optimization framework to the generalized Lefschetz thimbles.
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Submitted 3 August, 2022;
originally announced August 2022.
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Experimental Investigation of the Hyperfine Structure of Tm I with Fourier Transform Spectroscopy Part B: in the NIR wavelength range from 700 nm to 2250 nm
Authors:
Taha Yusuf Kebapcı,
Sami Sert,
Şeyma Parlatan,
İpek Kanat Öztürk,
Gönül Başar,
Günay Başar,
Maris Tamanis,
Sophie Kröger
Abstract:
In this study, we investigated the hyperfine structure of 43 spectral lines of atomic thulium. We analyzed Fourier-transform spectra in the wavelength range from 700 nm to 2250 nm, which corresponds to the wavenumber range from 14300 cm-1 to 4440 cm-1, respectively. The excited thulium atoms were generated in a hollow-cathode lamp. As a result of this investigation, the magnetic-dipole hyperfine c…
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In this study, we investigated the hyperfine structure of 43 spectral lines of atomic thulium. We analyzed Fourier-transform spectra in the wavelength range from 700 nm to 2250 nm, which corresponds to the wavenumber range from 14300 cm-1 to 4440 cm-1, respectively. The excited thulium atoms were generated in a hollow-cathode lamp. As a result of this investigation, the magnetic-dipole hyperfine constant A of 17 fine structure levels have been determined experimentally, 14 of them for the first time. The magnetic-dipole hyperfine constant values of the three remaining levels, reported in the literature, differed significantly from the results of our determination.
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Submitted 5 April, 2022;
originally announced April 2022.
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Experimental Investigation of the Hyperfine Structure of Tm I with Fourier Transform Spectroscopy, Part A: in the visible wavelength range 400 nm 700 nm
Authors:
Seyma Parlatan,
Ipek Kanat Ozturk,
Gonul Basar,
Gunay Basar,
Ruvin Ferber,
Sophie Kroger
Abstract:
The spectra emitted by a thulium hollow-cathode discharge lamp with argon or neon as inert gases have been recorded with a Bruker IFS 125 HR Fourier Transform spectrometer in the visible wavelength region from 400 nm to 700 nm. The paper presents the investigation of the hyperfine-structure splitting of 50 spectral lines of neutral thulium. As a result, the magnetic dipole hyperfine structure cons…
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The spectra emitted by a thulium hollow-cathode discharge lamp with argon or neon as inert gases have been recorded with a Bruker IFS 125 HR Fourier Transform spectrometer in the visible wavelength region from 400 nm to 700 nm. The paper presents the investigation of the hyperfine-structure splitting of 50 spectral lines of neutral thulium. As a result, the magnetic dipole hyperfine structure constant A for 20 fine structure levels of Tm I have been determined for the first time.
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Submitted 5 April, 2022;
originally announced April 2022.
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Uniformizing Lee-Yang Singularities
Authors:
Gokce Basar,
Gerald Dunne,
Zelong Yin
Abstract:
Motivated by the search for the QCD critical point, we discuss how to obtain the singular behavior of a thermodynamic system near a critical point, namely the Lee-Yang singularities, from a limited amount of local data generated in a different region of the phase diagram. We show that by using a limited number of Taylor series coefficients, it is possible to reconstruct the equation of state past…
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Motivated by the search for the QCD critical point, we discuss how to obtain the singular behavior of a thermodynamic system near a critical point, namely the Lee-Yang singularities, from a limited amount of local data generated in a different region of the phase diagram. We show that by using a limited number of Taylor series coefficients, it is possible to reconstruct the equation of state past the radius of convergence, in particular in the critical region. Furthermore we also show that it is possible to extend this reconstruction to go from a crossover region to the first-order transition region in the phase diagram, using a uniformizing map to pass between Riemann sheets. We illustrate these ideas via the Chiral Random Matrix Model and the Ising Model.
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Submitted 28 December, 2021;
originally announced December 2021.
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Universality, Lee-Yang singularities and series expansions
Authors:
Gokce Basar
Abstract:
We introduce a new way of reconstructing the equation of state of a thermodynamic system near a second order critical point from a finite set of Taylor coefficients computed away from the critical point. We focus on the Ising universality class (${\mathbb Z}_2$ symmetry) and show that in the crossover region of the phase diagram it is possible to efficiently extract the location of the nearest the…
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We introduce a new way of reconstructing the equation of state of a thermodynamic system near a second order critical point from a finite set of Taylor coefficients computed away from the critical point. We focus on the Ising universality class (${\mathbb Z}_2$ symmetry) and show that in the crossover region of the phase diagram it is possible to efficiently extract the location of the nearest thermodynamic singularity, the Lee-Yang edge singularity, from which one can (i) determine the location of the critical point, (ii) constrain the non-universal parameters that maps the equation of state to that of the Ising model in the scaling regime, and (iii) numerically evaluate the equation of state in the vicinity of the critical point. This is done by using a combination of Padé resummation and conformal maps. We explicitly demonstrate these ideas in the celebrated Gross-Neveu model.
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Submitted 15 June, 2021; v1 submitted 17 May, 2021;
originally announced May 2021.
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Evolution of Non-Gaussian Hydrodynamic Fluctuations
Authors:
Xin An,
Gokce Basar,
Mikhail Stephanov,
Ho-Ung Yee
Abstract:
In the context of the search for the QCD critical point using non-Gaussian fluctuations, we obtain the evolution equations for non-Gaussian cumulants to the leading order of the systematic expansion in the magnitude of thermal fluctuations. We develop a diagrammatic technique in which the leading order contributions are given by tree diagrams. We introduce a Wigner transform for multipoint correla…
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In the context of the search for the QCD critical point using non-Gaussian fluctuations, we obtain the evolution equations for non-Gaussian cumulants to the leading order of the systematic expansion in the magnitude of thermal fluctuations. We develop a diagrammatic technique in which the leading order contributions are given by tree diagrams. We introduce a Wigner transform for multipoint correlators and derive the evolution equations for three- and four-point Wigner functions for the problem of nonlinear stochastic diffusion with multiplicative noise.
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Submitted 13 August, 2021; v1 submitted 22 September, 2020;
originally announced September 2020.
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Complex Paths Around The Sign Problem
Authors:
Andrei Alexandru,
Gokce Basar,
Paulo F. Bedaque,
Neill C. Warrington
Abstract:
The Monte Carlo evaluation of path integrals is one of a few general purpose methods to approach strongly coupled systems. It is used in all branches of Physics, from QCD/nuclear physics to the correlated electron systems. However, many systems of great importance (dense matter inside neutron stars, the repulsive Hubbard model away from half-filling, dynamical and non-equilibrium observables) are…
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The Monte Carlo evaluation of path integrals is one of a few general purpose methods to approach strongly coupled systems. It is used in all branches of Physics, from QCD/nuclear physics to the correlated electron systems. However, many systems of great importance (dense matter inside neutron stars, the repulsive Hubbard model away from half-filling, dynamical and non-equilibrium observables) are not amenable to the Monte Carlo method as it currently stands due to the so-called "sign-problem". We review a new set of ideas recently developed to tackle the sign problem based on the complexification of field space and the Picard-Lefshetz theory accompanying it. The mathematical ideas underpinning this approach, as well as the algorithms so far developed, are described together with non-trivial examples where the method has already been proved successful. Directions of future work, including the burgeoning use of machine learning techniques, are delineated.
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Submitted 10 July, 2020;
originally announced July 2020.
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Fluctuation dynamics in a relativistic fluid with a critical point
Authors:
Xin An,
Gokce Basar,
Mikhail Stephanov,
Ho-Ung Yee
Abstract:
To describe dynamics of bulk and fluctuations near the QCD critical point we develop general relativistic fluctuation formalism for a fluid carrying baryon charge. Feedback of fluctuations modifies hydrodynamic coefficients including bulk viscosity and conductivity and introduces nonlocal and non-instantaneous terms in constitutive equations. We perform necessary ultraviolet (short-distance) renor…
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To describe dynamics of bulk and fluctuations near the QCD critical point we develop general relativistic fluctuation formalism for a fluid carrying baryon charge. Feedback of fluctuations modifies hydrodynamic coefficients including bulk viscosity and conductivity and introduces nonlocal and non-instantaneous terms in constitutive equations. We perform necessary ultraviolet (short-distance) renormalization to obtain cutoff independent deterministic equations suitable for numerical implementation. We use the equations to calculate the universal non-analytic small-frequency dependence of transport coefficients due to fluctuations (long-time tails). Focusing on the critical mode we show how this general formalism matches existing Hydro+ description of fluctuations near the QCD critical point and nontrivially extends it inside and outside of the critical region.
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Submitted 31 December, 2019;
originally announced December 2019.
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Relativistic Hydrodynamic Fluctuations
Authors:
Xin An,
Gokce Basar,
Mikhail Stephanov,
Ho-Ung Yee
Abstract:
We present a general systematic formalism for describing dynamics of fluctuations in an arbitrary relativistic hydrodynamic flow, including their feedback (known as long-time hydrodynamic tails). The fluctuations are described by two-point equal-time correlation functions. We introduce a definition of equal time in a situation where the local rest frame is determined by the local flow velocity, an…
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We present a general systematic formalism for describing dynamics of fluctuations in an arbitrary relativistic hydrodynamic flow, including their feedback (known as long-time hydrodynamic tails). The fluctuations are described by two-point equal-time correlation functions. We introduce a definition of equal time in a situation where the local rest frame is determined by the local flow velocity, and a method of taking derivatives and Wigner transforms of such equal-time correlation functions, which we call confluent. We find that the equations for confluent Wigner functions not only resemble kinetic equations, but that the kinetic equation for phonons propagating on an arbitrary background nontrivially matches the equations for Wigner functions, including relativistic inertial and Coriolis forces due to acceleration and vorticity of the flow. We also describe the procedure of renormalization of short-distance singularities which eliminates cutoff dependence, allowing efficient numerical implementation of these equations.
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Submitted 29 March, 2019; v1 submitted 25 February, 2019;
originally announced February 2019.
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Finite Density $QED_{1+1}$ Near Lefschetz Thimbles
Authors:
Andrei Alexandru,
Gokce Basar,
Paulo F. Bedaque,
Henry Lamm,
Scott Lawrence
Abstract:
One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination of Lefschetz thimbles -- or somewhat close to them -- the sign problem is alleviated. Gauge theories lack a well-defined thimble decomposition, and therefore it is unclear how to carry out a generaliz…
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One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination of Lefschetz thimbles -- or somewhat close to them -- the sign problem is alleviated. Gauge theories lack a well-defined thimble decomposition, and therefore it is unclear how to carry out a generalized thimble method. In this paper we discuss some of the conceptual issues involved by applying this method to $QED_{1+1}$ at finite density, showing that the generalized thimble method yields correct results with less computational effort than standard methods.
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Submitted 5 July, 2018;
originally announced July 2018.
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A Primer on Resurgent Transseries and Their Asymptotics
Authors:
Inês Aniceto,
Gökçe Başar,
Ricardo Schiappa
Abstract:
The computation of observables in general interacting theories, be them quantum mechanical, field, gauge or string theories, is a non-trivial problem which in many cases can only be addressed by resorting to perturbative methods. In most physically interesting problems these perturbative expansions result in asymptotic series with zero radius of convergence. These asymptotic series then require th…
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The computation of observables in general interacting theories, be them quantum mechanical, field, gauge or string theories, is a non-trivial problem which in many cases can only be addressed by resorting to perturbative methods. In most physically interesting problems these perturbative expansions result in asymptotic series with zero radius of convergence. These asymptotic series then require the use of resurgence and transseries in order for the associated observables to become nonperturbatively well-defined. Resurgence encodes the complete large-order asymptotic behaviour of the coefficients from a perturbative expansion, generically in terms of (multi) instanton sectors and for each problem in terms of its Stokes constants. Some observables arise from linear problems, and have a finite number of instanton sectors and associated Stokes constants; some other observables arise from nonlinear problems, and have an infinite number of instanton sectors and Stokes constants. By means of two very explicit examples, and with emphasis on a pedagogical style of presentation, this work aims at serving as a primer on the aforementioned resurgent, large-order asymptotics of general perturbative expansions. This includes discussions of transseries, Stokes phenomena, generalized steepest-descent methods, Borel transforms, nonlinear resonance, and alien calculus. Furthermore, resurgent properties of transseries---usually described mathematically via alien calculus---are recast in equivalent physical languages: either a "statistical mechanical" language, as motions in chains and lattices; or a "conformal field theoretical" language, with underlying Virasoro-like algebraic structures.
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Submitted 31 January, 2019; v1 submitted 28 February, 2018;
originally announced February 2018.
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Schwinger-Keldysh on the lattice: a faster algorithm and its application to field theory
Authors:
Andrei Alexandru,
Gokce Basar,
Paulo F. Bedaque,
Gregory W. Ridgway
Abstract:
A new algorithm is developed allowing the Monte Carlo study of a 1 + 1 dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This improvement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from O(N^3) to less than O(N^2). As an additional…
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A new algorithm is developed allowing the Monte Carlo study of a 1 + 1 dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This improvement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from O(N^3) to less than O(N^2). As an additional feature, the algorithm leads to improved Monte Carlo proposals. We exemplify the use of the algorithm to the real time dynamics of a scalar φ^4 theory with weak and strong couplings.
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Submitted 31 May, 2017; v1 submitted 21 April, 2017;
originally announced April 2017.
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Interplay of Reggeon and photon in pA collisions
Authors:
Gokce Basar,
Dmitri Kharzeev,
Ho-Ung Yee,
Ismail Zahed
Abstract:
We discuss the effects of the electromagnetic interaction in high-energy proton collisions with nuclei of large Z at strong coupling $λ=g^2N_c$. Using the holographic dual limit of large $N_c>λ\gg 1$, we describe the Reggeon exchange as a twisted surface and show that it gets essentially modified by the electromagnetic interaction.
We discuss the effects of the electromagnetic interaction in high-energy proton collisions with nuclei of large Z at strong coupling $λ=g^2N_c$. Using the holographic dual limit of large $N_c>λ\gg 1$, we describe the Reggeon exchange as a twisted surface and show that it gets essentially modified by the electromagnetic interaction.
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Submitted 17 March, 2017;
originally announced March 2017.
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Tempered transitions between thimbles
Authors:
Andrei Alexandru,
Gokce Basar,
Paulo F. Bedaque,
Neill C. Warrington
Abstract:
Quantum field theories with complex actions cannot be investigated using importance sampling due to the sign problem. One possible solution is to use the holomorphic gradient flow, a method we introduced related to the Lefschetz thimbles idea. In many cases the probability distribution generated by this method is multi-modal and standard Monte-Carlo sampling fails. We propose an algorithm that inc…
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Quantum field theories with complex actions cannot be investigated using importance sampling due to the sign problem. One possible solution is to use the holomorphic gradient flow, a method we introduced related to the Lefschetz thimbles idea. In many cases the probability distribution generated by this method is multi-modal and standard Monte-Carlo sampling fails. We propose an algorithm that incorporates tempered proposals to solve this problem. We apply this algorithm to the 0+1 dimensional Thirring model at finite density for a parameter set where standard sampling fails and show that tempered proposals cure this problem.
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Submitted 7 March, 2017;
originally announced March 2017.
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Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
Authors:
Gokce Basar,
Gerald V. Dunne,
Mithat Unsal
Abstract:
For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the a…
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For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential. These are related to the Chebyshev potentials, which are in turn related to certain ${\mathcal N}=2$ supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological $c=3$ Landau-Ginzburg models and `special geometry'. These systems inherit a natural modular structure corresponding to Ramanujan's theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Our approach is very elementary, using basic classical geometry combined with all-orders WKB.
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Submitted 23 January, 2017;
originally announced January 2017.
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Monte Carlo calculations of the finite density Thirring model
Authors:
Andrei Alexandru,
Gokce Basar,
Paulo F. Bedaque,
Gregory W. Ridgway,
Neill C. Warrington
Abstract:
We present results of the numerical simulation of the two-dimensional Thirring model at finite density and temperature. The severe sign problem is dealt with by deforming the domain of integration into complex field space. This is the first example where a fermionic sign problem is solved in a quantum field theory by using the holomorphic gradient flow approach, a generalization of the Lefschetz t…
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We present results of the numerical simulation of the two-dimensional Thirring model at finite density and temperature. The severe sign problem is dealt with by deforming the domain of integration into complex field space. This is the first example where a fermionic sign problem is solved in a quantum field theory by using the holomorphic gradient flow approach, a generalization of the Lefschetz thimble method.
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Submitted 18 September, 2016; v1 submitted 6 September, 2016;
originally announced September 2016.
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A study of symmetry breaking in a relativistic Bose gas using the contraction algorithm
Authors:
Andrei Alexandru,
Gokce Basar,
Paulo Bedaque,
Gregory W. Ridgway,
Neill C. Warrington
Abstract:
A relativistic Bose gas at finite density suffers from a sign problem that makes direct numerical simulations not feasible. One possible solution to the sign problem is to re-express the path integral in terms of Lefschetz thimbles. Using this approach we study the relativistic Bose gas both in the symmetric phase (low-density) and the spontaneously broken phase (high-density). In the high-density…
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A relativistic Bose gas at finite density suffers from a sign problem that makes direct numerical simulations not feasible. One possible solution to the sign problem is to re-express the path integral in terms of Lefschetz thimbles. Using this approach we study the relativistic Bose gas both in the symmetric phase (low-density) and the spontaneously broken phase (high-density). In the high-density phase we break explicitly the symmetry and determine the dependence of the order parameter on the breaking. We study the relative contributions of the dominant and sub-dominant thimbles in this phase. We find that the sub-dominant thimble only contributes substantially when the explicit symmetry breaking is small, a regime that is dominated by finite volume effects. In the regime relevant for the thermodynamic limit, this contribution is negligible.
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Submitted 8 June, 2016;
originally announced June 2016.
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Monte Carlo study of real time dynamics
Authors:
Andrei Alexandru,
Gokce Basar,
Paulo F. Bedaque,
Sohan Vartak,
Neill C. Warrington
Abstract:
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the ph…
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Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and in principle applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.
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Submitted 10 June, 2016; v1 submitted 25 May, 2016;
originally announced May 2016.
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Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles
Authors:
Andrei Alexandru,
Gokce Basar,
Paulo F. Bedaque,
Gregory W. Ridgway,
Neill C. Warrington
Abstract:
A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen sub-manifolds ("thimbles") the sign problem disappears or is drastically alleviated. The parametrization of the thimble by real coordinates require the calcula…
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A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen sub-manifolds ("thimbles") the sign problem disappears or is drastically alleviated. The parametrization of the thimble by real coordinates require the calculation of a jacobian with a computational cost of order O(V^3), where V is proportional to the spacetime volume. In this note we propose two estimators for this jacobian with a computational cost of order O(V). We discuss analytically the regimes where we expect the estimator to work and show numerical examples in two different models.
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Submitted 4 April, 2016;
originally announced April 2016.
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Sign problem and Monte Carlo calculations beyond Lefschetz thimbles
Authors:
Andrei Alexandru,
Gokce Basar,
Paulo F. Bedaque,
Gregory W. Ridgway,
Neill C. Warrington
Abstract:
We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action. We describe a family of such manifolds that interpolate between the tangent space at one critical point, where the sign problem is milder compared to the real plane but in some cases still severe,…
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We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action. We describe a family of such manifolds that interpolate between the tangent space at one critical point, where the sign problem is milder compared to the real plane but in some cases still severe, and the union of relevant thimbles, where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling. We exemplify this approach using a simple 0 + 1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefshetz thimbles was elusive.
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Submitted 21 March, 2016; v1 submitted 29 December, 2015;
originally announced December 2015.
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Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter
Authors:
Gökçe Başar,
Aleksey Cherman,
Keith R. Dienes,
David A. McGady
Abstract:
In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-$N$ limit. This was done within the tractable setting in which the gauge theory is compactified on a three-sphere whose radius is small compared to the strong length scale. In this pap…
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In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-$N$ limit. This was done within the tractable setting in which the gauge theory is compactified on a three-sphere whose radius is small compared to the strong length scale. In this paper, we generalize these observations by demonstrating that similar results continue to hold even when massless adjoint matter fields are introduced. These results hold for both thermal and $(-1)^F$-twisted partition functions, and collectively suggest that the spectra of large-$N$ confining gauge theories are organized by the symmetries of two-dimensional conformal field theories.
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Submitted 24 December, 2015;
originally announced December 2015.
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A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
Authors:
Andrei Alexandru,
Gokce Basar,
Paulo Bedaque
Abstract:
A possible solution of the notorious sign problem preventing direct Monte Carlo calculations for systems with non-zero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We investigate this approach for a simple fermionic model. We introduce an easy to implement Monte Carlo algorithm to sample the dominant thimble. Our algorithm relies only on the i…
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A possible solution of the notorious sign problem preventing direct Monte Carlo calculations for systems with non-zero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We investigate this approach for a simple fermionic model. We introduce an easy to implement Monte Carlo algorithm to sample the dominant thimble. Our algorithm relies only on the integration of the gradient flow in the numerically stable direction, which gives it a distinct advantage over the other proposed algorithms. We demonstrate the stability and efficiency of the algorithm by applying it to an exactly solvable fermionic model and compare our results with the analytical ones. We report a very good agreement for a certain region in the parameter space where the dominant contribution comes from a single thimble, including a region where standard methods suffer from a severe sign problem. However, we find that there are also regions in the parameter space where the contribution from multiple thimbles is important, even in the continuum limit.
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Submitted 12 October, 2015;
originally announced October 2015.
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Hydrodynamics, resurgence and trans-asymptotics
Authors:
Gokce Basar,
Gerald V. Dunne
Abstract:
The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exp…
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The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with initial conditions.
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Submitted 16 September, 2015;
originally announced September 2015.
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A 4D-2D equivalence for large-N Yang-Mills theory
Authors:
Gokce Basar,
Aleksey Cherman,
Keith R. Dienes,
David A. McGady
Abstract:
General string-theoretic considerations suggest that four-dimensional large-N gauge theories should have dual descriptions in terms of two-dimensional conformal field theories. However, for non-supersymmetric confining theories such as pure Yang-Mills theory, a long-standing challenge has been to explicitly show that such dual descriptions actually exist. In this paper, we consider the large-N lim…
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General string-theoretic considerations suggest that four-dimensional large-N gauge theories should have dual descriptions in terms of two-dimensional conformal field theories. However, for non-supersymmetric confining theories such as pure Yang-Mills theory, a long-standing challenge has been to explicitly show that such dual descriptions actually exist. In this paper, we consider the large-N limit of four-dimensional pure Yang-Mills theory compactified on a three-sphere in the solvable limit where the sphere radius is small compared to the strong length scale, and demonstrate that the confined-phase spectrum of this gauge theory coincides with the spectrum of an irrational two-dimensional conformal field theory.
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Submitted 10 August, 2015; v1 submitted 30 July, 2015;
originally announced July 2015.
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Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
Authors:
Gokce Basar,
Gerald V. Dunne
Abstract:
The Nekrasov-Shatashvili limit for the low-energy behavior of N=2 and N=2* supersymmetric SU(2) gauge theories is encoded in the spectrum of the Mathieu and Lam'e equations, respectively. This correspondence is usually expressed via an all-orders Bohr-Sommerfeld relation, but this neglects non-perturbative effects, the nature of which is very different in the electric, magnetic and dyonic regions.…
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The Nekrasov-Shatashvili limit for the low-energy behavior of N=2 and N=2* supersymmetric SU(2) gauge theories is encoded in the spectrum of the Mathieu and Lam'e equations, respectively. This correspondence is usually expressed via an all-orders Bohr-Sommerfeld relation, but this neglects non-perturbative effects, the nature of which is very different in the electric, magnetic and dyonic regions. In the gauge theory dyonic region the spectral expansions are divergent, and indeed are not Borel-summable, so they are more properly described by resurgent trans-series in which perturbative and non-perturbative effects are deeply entwined. In the gauge theory electric region the spectral expansions are convergent, but nevertheless there are non-perturbative effects due to poles in the expansion coefficients, and which we associate with worldline instantons. This provides a concrete analog of a phenomenon found recently by Drukker, Marino and Putrov in the large N expansion of the ABJM matrix model, in which non-perturbative effects are related to complex space-time instantons. In this paper we study how these very different regimes arise from an exact WKB analysis, and join smoothly through the magnetic region. This approach also leads to a simple proof of a resurgence relation found recently by Dunne and Unsal, showing that for these spectral systems all non-perturbative effects are subtly encoded in perturbation theory, and identifies this with the Picard-Fuchs equation for the quantized elliptic curve.
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Submitted 22 January, 2015;
originally announced January 2015.
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Bose-Fermi Degeneracies in Large $N$ Adjoint QCD
Authors:
Gokce Basar,
Aleksey Cherman,
David A. McGady
Abstract:
We analyze the large $N$ limit of adjoint QCD, an $SU(N)$ gauge theory with $N_f$ flavors of massless adjoint Majorana fermions, compactified on $S^3 \times S^1$. We focus on the weakly-coupled confining small-$S^3$ regime. If the fermions are given periodic boundary conditions on $S^1$, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition…
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We analyze the large $N$ limit of adjoint QCD, an $SU(N)$ gauge theory with $N_f$ flavors of massless adjoint Majorana fermions, compactified on $S^3 \times S^1$. We focus on the weakly-coupled confining small-$S^3$ regime. If the fermions are given periodic boundary conditions on $S^1$, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any $S^1$ size $L$, even though the bosonic and fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in the confining phase for any $L \sim N^0$, explaining how it is able to enjoy large $N$ volume independence for any $L$. The large $N$ boson-fermion cancellations take place in a setting where adjoint QCD is manifestly non-supersymmetric at any finite $N$, and are consistent with the recent conjecture that adjoint QCD has emergent fermionic symmetries in the large $N$ limit.
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Submitted 24 March, 2015; v1 submitted 4 September, 2014;
originally announced September 2014.
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A scaling relation between proton-nucleus and nucleus-nucleus collisions
Authors:
Gokce Basar,
Derek Teaney
Abstract:
It is recently discovered that at high multiplicy, the proton-nucleus ($pA$) collisions give rise to two particle correlations that are strikingly similar to those of nucleus-nucleus ($AA$) collisions at the same multiplicity, although the system size is smaller in $pA$. Using an independent cluster model and a simple conformal scaling argument, where the ratio of the mean free path to the system…
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It is recently discovered that at high multiplicy, the proton-nucleus ($pA$) collisions give rise to two particle correlations that are strikingly similar to those of nucleus-nucleus ($AA$) collisions at the same multiplicity, although the system size is smaller in $pA$. Using an independent cluster model and a simple conformal scaling argument, where the ratio of the mean free path to the system size stays constant at fixed multiplicity, we argue that flow in $pA$ emerges as a collective response to the fluctuations in the position of clusters, just like in $AA$ collisions. With several physically motivated and parameter free rescalings of the recent LHC data, we show that this simple model captures the essential physics of elliptic and triangular flow in $pA$ collisions.
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Submitted 14 August, 2014;
originally announced August 2014.
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Casimir energy of confining large $N$ gauge theories
Authors:
Gokce Basar,
Aleksey Cherman,
David A. McGady,
Masahito Yamazaki
Abstract:
Four-dimensional asymptotically-free large $N$ gauge theories compactified on $S^3_R \times \mathbb{R}$ have a weakly-coupled confining regime when $R$ is small compared to the strong scale. We compute the vacuum energy of a variety of confining large $N$ non-supersymmetric gauge theories in this calculable regime, where the vacuum energy can be thought of as the $S^3$ Casimir energy. The…
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Four-dimensional asymptotically-free large $N$ gauge theories compactified on $S^3_R \times \mathbb{R}$ have a weakly-coupled confining regime when $R$ is small compared to the strong scale. We compute the vacuum energy of a variety of confining large $N$ non-supersymmetric gauge theories in this calculable regime, where the vacuum energy can be thought of as the $S^3$ Casimir energy. The $N=\infty$ renormalized vacuum energy turns out to vanish in all of the large $N$ gauge theories we have examined, confirming a striking prediction of temperature-reflection symmetry.
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Submitted 11 November, 2014; v1 submitted 13 August, 2014;
originally announced August 2014.
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T-Reflection
Authors:
Gokce Basar,
Aleksey Cherman,
David A. McGady,
Masahito Yamazaki
Abstract:
We point out the presence of a $T \to -T$ temperature-reflection ($T$-reflection) symmetry for the partition functions of many physical systems. Without knowledge of the origin of the symmetry, we have only been able to test the existence of $T$-reflection symmetry in systems with exactly-calculable partition functions. We show that $T$-reflection symmetry is present in a variety of conformal and…
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We point out the presence of a $T \to -T$ temperature-reflection ($T$-reflection) symmetry for the partition functions of many physical systems. Without knowledge of the origin of the symmetry, we have only been able to test the existence of $T$-reflection symmetry in systems with exactly-calculable partition functions. We show that $T$-reflection symmetry is present in a variety of conformal and non-conformal field theories and statistical mechanics models with known partition functions. For example, all minimal model partition functions in two-dimensional conformal field theories are invariant under $T$-reflections. An interesting property of the $T$-reflection symmetry is that it can be broken by shifts of the vacuum energy.
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Submitted 15 July, 2014; v1 submitted 24 June, 2014;
originally announced June 2014.
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The Magneto-Sono-Luminescence and its signatures in photon and dilepton production in heavy ion collisions
Authors:
Gokce Basar,
Dmitri E. Kharzeev,
Edward V. Shuryak
Abstract:
The matter produced in the early stages of heavy ion collisions consists mostly of gluons, and is penetrated by coherent magnetic field produced by spectator nucleons. The fluctuations of gluonic matter in an external magnetic field couple to real and virtual photons through virtual quark loops. We study the resulting contributions to photon and dilepton production that stem from the fluctuations…
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The matter produced in the early stages of heavy ion collisions consists mostly of gluons, and is penetrated by coherent magnetic field produced by spectator nucleons. The fluctuations of gluonic matter in an external magnetic field couple to real and virtual photons through virtual quark loops. We study the resulting contributions to photon and dilepton production that stem from the fluctuations of the stress tensor $T_{μν}$ in the background of a coherent magnetic field $\vec{B}$. Our study extends significantly the earlier work by two of us and Skokov, in which only the fluctuations of the trace of the stress tensor $T_{μμ}$ were considered (the coupling of $T_{μμ}$ to electromagnetic fields is governed by the scale anomaly). In the present paper we derive more general relations using the Operator Product Expansion (OPE). We also extend the previous study to the case of dileptons which offers the possibility to discriminate between various production mechanisms. Among the phenomena that we study are Magneto-Sono-Luminescence (MSL, the interaction of magnetic field $\vec{B}(x,t)$ with the sound perturbations of the stress tensor $δT_{μν}(x,t)$) and Magneto-Thermo-Luminescence (MTL, the interaction of $\vec{B}(x,t)$ with smooth average $<T_{μν}>$). We calculate the rates of these process and find that they can dominate the photon and dilepton production at early stage of heavy ion collisions. We also point out the characteristic signatures of MSL and MTL that can be used to establish their presence and to diagnose the produced matter.
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Submitted 28 March, 2014; v1 submitted 10 February, 2014;
originally announced February 2014.
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A scaling relation between pA and AA collisions
Authors:
Gokce Basar,
Derek Teaney
Abstract:
We compare the flow-like correlations in high multiplicity proton-nucleus ($p+A$) and nucleus-nucleus ($A+A$) collisions. At fixed multiplicity, the correlations in these two colliding systems are strikingly similar, although the system size is smaller in $p+A$. Based on an independent cluster model and a simple conformal scaling argument, where the ratio of the mean free path to the system size s…
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We compare the flow-like correlations in high multiplicity proton-nucleus ($p+A$) and nucleus-nucleus ($A+A$) collisions. At fixed multiplicity, the correlations in these two colliding systems are strikingly similar, although the system size is smaller in $p+A$. Based on an independent cluster model and a simple conformal scaling argument, where the ratio of the mean free path to the system size stays constant at fixed multiplicity, we argue that flow in $p+A$ emerges as a collective response to the fluctuations in the position of clusters, just like in $A+A$ collisions. With several physically motivated and parameter free rescalings of the recent LHC data, we show that this simple model captures the essential physics of elliptic and triangular flow in $p+A$ collisions. We also explore the implications of the model for jet energy loss in $p+A$, and predict slightly larger transverse momentum broadening in $p+A$ than in $A+A$ at the same multiplicity.
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Submitted 13 August, 2014; v1 submitted 24 December, 2013;
originally announced December 2013.
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Resurgence theory, ghost-instantons, and analytic continuation of path integrals
Authors:
Gokce Basar,
Gerald V. Dunne,
Mithat Unsal
Abstract:
A general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic analysis implies that both types of saddles contribute to physical observables, even if the complex saddles are not on the integration path i.e., the associated Stokes multipliers are zero. We show explicitly tha…
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A general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic analysis implies that both types of saddles contribute to physical observables, even if the complex saddles are not on the integration path i.e., the associated Stokes multipliers are zero. We show explicitly that instanton-anti-instanton and ghost--anti-ghost saddles both affect the expansion around the perturbative vacuum. We study a self-dual model in which the analytic continuation of the partition function to negative values of coupling constant gives a pathological exponential growth, but a homotopically independent combination of integration cycles (Lefschetz thimbles) results in a sensible theory. These two choices of the integration cycles are tied with a quantum phase transition. The general set of ideas in our construction may provide new insights into non-perturbative QFT, string theory, quantum gravity, and the theory of quantum phase transitions.
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Submitted 23 August, 2013; v1 submitted 5 August, 2013;
originally announced August 2013.
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Chiral and Gravitational Anomalies on Fermi Surfaces
Authors:
Gokce Basar,
Dmitri E. Kharzeev,
Ismail Zahed
Abstract:
A Fermi surface threaded by a Berry phase can be described by the Wess-Zumino-Witten (WZW) term. After gauging, it produces a five-dimensional Chern-Simons term in the action. We show how this Chern-Simons term captures the essence of the Abelian, non-Abelian, and mixed gravitational anomalies in describing both in- and off-equilibrium phenomena. In particular we derive a novel contribution to the…
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A Fermi surface threaded by a Berry phase can be described by the Wess-Zumino-Witten (WZW) term. After gauging, it produces a five-dimensional Chern-Simons term in the action. We show how this Chern-Simons term captures the essence of the Abelian, non-Abelian, and mixed gravitational anomalies in describing both in- and off-equilibrium phenomena. In particular we derive a novel contribution to the Chiral Vortical Effect that arises when a temperature gradient is present. We also discuss the issue of universality of the anomalous currents.
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Submitted 8 July, 2013;
originally announced July 2013.
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Large N Volume Independence and an Emergent Fermionic Symmetry
Authors:
Gokce Basar,
Aleksey Cherman,
Daniele Dorigoni,
Mithat Unsal
Abstract:
Large-N volume independence in circle-compactified QCD with N_f \geq 1 adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories are believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically…
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Large-N volume independence in circle-compactified QCD with N_f \geq 1 adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories are believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically implies a phase transition at some finite radius. This tension is resolved if there are degeneracies between the spectra of bosonic and fermionic states, as happens in the N_f=1 supersymmetric case. Resolution of the tension for N_f>1 then suggests the emergence of a fermionic symmetry at large N, where there is no supersymmetry. We can escape the Coleman-Mandula theorem since the N=\infty theory is free, with a trivial S-matrix. We show an example of such a spectral degeneracy in a non-supersymmetric toy example which has a Hagedorn spectrum.
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Submitted 21 January, 2014; v1 submitted 12 June, 2013;
originally announced June 2013.
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Triangle anomaly in Weyl semi-metals
Authors:
Gokce Basar,
Dmitri E. Kharzeev,
Ho-Ung Yee
Abstract:
Weyl semimetals possess massless chiral quasi-particles, and are thus affected by the triangle anomalies. We discuss the features of the chiral magnetic and chiral vortical effects specific to Weyl semimetals, and then propose three novel phenomena caused by the triangle anomalies in this material: 1) anomaly cooling; 2) charge transport by soliton waves as described by the Burgers' equation, and…
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Weyl semimetals possess massless chiral quasi-particles, and are thus affected by the triangle anomalies. We discuss the features of the chiral magnetic and chiral vortical effects specific to Weyl semimetals, and then propose three novel phenomena caused by the triangle anomalies in this material: 1) anomaly cooling; 2) charge transport by soliton waves as described by the Burgers' equation, and 3) the shift of the BKT phase transition of superfluid vortices coupled to Weyl fermions. In addition, we establish the conditions under which the chiral magnetic current exists in real materials.
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Submitted 8 January, 2014; v1 submitted 27 May, 2013;
originally announced May 2013.