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Quantum chaos and late-time equipartition of symmetry-resolved Krylov complexity
Authors:
Jayashish Das,
Suman Das,
Juan F. Pedraza,
Le-Chen Qu
Abstract:
We study symmetry-resolved Krylov complexity in finite-dimensional chaotic quantum many-body systems. When both the Hamiltonian and the initial operator commute with a conserved charge, the operator dynamics decomposes into independent symmetry sectors, each with its own Krylov chain. We show that, after saturation, the unresolved Krylov complexity is additive over symmetry sectors. In the absence…
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We study symmetry-resolved Krylov complexity in finite-dimensional chaotic quantum many-body systems. When both the Hamiltonian and the initial operator commute with a conserved charge, the operator dynamics decomposes into independent symmetry sectors, each with its own Krylov chain. We show that, after saturation, the unresolved Krylov complexity is additive over symmetry sectors. In the absence of additional Liouvillian degeneracies, the late-time contribution of a sector with Hilbert-space dimension $d_q$ is controlled by $d_q(d_q-1)$, leading to a dimension-weighted equipartition that approaches the simple large-sector scaling $d_q^2/\sum_{q'}d_{q'}^2$. This late-time rule differs from the early-time weighted-average discussed in the literature and is governed instead by the dimensions of the accessible operator spaces. We support the analytic prediction with numerical studies of the real and complex SYK models, a chaotic bosonic spin model, and the mixed-field Ising chain. Our results show that resolving exact symmetries is essential for interpreting the saturation value of Krylov complexity as a diagnostic of chaotic operator growth.
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Submitted 19 August, 2026;
originally announced August 2026.
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Symmetry Resolved Entanglement Entropy: Equipartition under Driven and Non-unitary Evolution in a Compact Boson CFT
Authors:
Filiberto Ares,
Jayashish Das,
Arnab Kundu
Abstract:
We study the evolution of symmetry-resolved entanglement entropy in bulk-driven Floquet conformal field theories (CFTs). Focusing on the two-dimensional free compact boson CFT, we analyze how symmetry-resolved Rényi entropies approach or depart from equipartition among charge sectors. We show that the existence of an $\mathfrak{sl}^{(k)}(2,\mathbb{R})$ subalgebra of the Virasoro algebra introduces…
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We study the evolution of symmetry-resolved entanglement entropy in bulk-driven Floquet conformal field theories (CFTs). Focusing on the two-dimensional free compact boson CFT, we analyze how symmetry-resolved Rényi entropies approach or depart from equipartition among charge sectors. We show that the existence of an $\mathfrak{sl}^{(k)}(2,\mathbb{R})$ subalgebra of the Virasoro algebra introduces a free parameter, the label $k$, which allows us to control the breakdown of equipartition. We argue that this effect originates from an explicit coupling between low- and high-frequency modes. Based on a general oscillator representation of the Virasoro algebra, we expect this mechanism to persist beyond the free boson CFT. Finally, we discuss how the real-time dynamics of fine-grained symmetry-resolved entropies of a boundary state are modified under non-unitary evolution, which can be associated with post-selected weak measurements.
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Submitted 30 March, 2026;
originally announced March 2026.
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Flipped Rotating Axion Non-minimally Coupled to Gravity: Baryogenesis and Dark Matter
Authors:
Chao Chen,
Suruj Jyoti Das,
Konstantinos Dimopoulos,
Anish Ghoshal
Abstract:
We demonstrate that the co-genesis of baryon asymmetry and dark matter can be achieved through the rotation of an axion-like particle, driven by a flip in the vacuum manifold's direction at the end of inflation. This can occur if the axion has a periodic non-minimal coupling to gravity, while preserving the discrete shift symmetry. In non-oscillating inflation models, after inflation there is typi…
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We demonstrate that the co-genesis of baryon asymmetry and dark matter can be achieved through the rotation of an axion-like particle, driven by a flip in the vacuum manifold's direction at the end of inflation. This can occur if the axion has a periodic non-minimal coupling to gravity, while preserving the discrete shift symmetry. In non-oscillating inflation models, after inflation there is typically a period of kination (with $w = 1$). In this case, it is shown that the vacuum manifold of the axion is flipped and the axion begins rotating in field space, because it can slide across the decreasing potential barrier as in Ricci reheating. Such a rotating axion can generate the baryon asymmetry of the Universe through spontaneous baryogenesis, while at later epochs it can oscillate as dark matter. The period of kination makes the primordial gravitational waves (GW) generated during inflation sharply blue-tilted which constrains the parameter space due to GW overproduction, while being testable by next generation CMB experiments. As a concrete example, we show that such a cogenesis of baryon asymmetry and dark matter can be realized for the axion as the Majoron in the Type-I seesaw setup, predicting mass ranges for the Majoron below sub eVs, with right-handed neutrino mass above $\mathcal{O}(10^{8})$ GeV. We also show that in order to avoid fragmentation of the axion condensate during the rotation, we require the non-minimal coupling $ξ\sim (f/m_P)^2 $ or somewhat larger, where $f$ is the axion decay constant.
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Submitted 1 September, 2025; v1 submitted 12 February, 2025;
originally announced February 2025.
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Two-loop dimension Six Effective Action: Integrating Out Heavy Scalar
Authors:
Nilabhra Adhikary,
Jaydeb Das,
Debmalya Dey
Abstract:
For the first time, we present the model-independent two-loop effective action up to dimension six after integrating out heavy scalar(s) employing the Heat-Kernel method. We compute the effective operators that emerge at two-loop for two example models: heavy electroweak complex Triplet and Doublet scalars. We present our results on the SILH basis. We also capture the effect in the fermion sector.…
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For the first time, we present the model-independent two-loop effective action up to dimension six after integrating out heavy scalar(s) employing the Heat-Kernel method. We compute the effective operators that emerge at two-loop for two example models: heavy electroweak complex Triplet and Doublet scalars. We present our results on the SILH basis. We also capture the effect in the fermion sector. For these two scenarios, we compute all the fermionic effective operators up to dimension six.
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Submitted 4 January, 2026; v1 submitted 2 January, 2025;
originally announced January 2025.
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Flowery Horizons & Bulk Observers: $sl^{(q)}(2,\mathbb{R})$ Drive in $2d$ Holographic CFT
Authors:
Jayashish Das,
Arnab Kundu
Abstract:
We explore and analyze bulk geometric aspects corresponding to a driven two-dimensional holographic CFT, where the drive Hamiltonian is constructed from the $sl^{(q)}(2,\mathbb{R})$ generators. In particular, we demonstrate that starting with a thermal initial state, the evolution of the event horizon is characterized by distinct geometric transformations in the bulk which are associated to the co…
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We explore and analyze bulk geometric aspects corresponding to a driven two-dimensional holographic CFT, where the drive Hamiltonian is constructed from the $sl^{(q)}(2,\mathbb{R})$ generators. In particular, we demonstrate that starting with a thermal initial state, the evolution of the event horizon is characterized by distinct geometric transformations in the bulk which are associated to the conjugacy classes of the corresponding transformations on the CFT. Namely, the bulk evolution of the horizon is geometrically classified into an oscillatory (non-heating) behaviour, an exponentially growing (heating) behaviour and a power-law growth with an angular rotation (the phase boundary), all as a function of the stroboscopic time. We also show that the explicit symmetry breaking of the drive is manifest in a flowery structure of the event horizon that displays a $U(1) \to {\mathbb Z}_q$ symmetry breaking. In the $q\to \infty$ limit, the $U(1)$ symmetry is effectively restored. Furthermore, by analyzing the integral curves generated by the asymptotic Killing vectors, we also demonstrate how the fixed points of these curves approximate a bulk Ryu-Takayanagi surface corresponding to a modular Hamiltonian for a sub-region in the CFT. Since the CFT modular Hamiltonian has an infinitely many in-equivalent extensions in the bulk, the fixed points of the integral curves can also lie outside the entanglement wedge of the CFT sub-region.
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Submitted 30 January, 2025; v1 submitted 24 December, 2024;
originally announced December 2024.
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Rethinking the Effective Field Theory formulation of Gravity
Authors:
Jesse Daas,
Cristobal Laporte,
Frank Saueressig,
Tim van Dijk
Abstract:
General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory is not fundamental though, but constitutes the lowest order term in an effective field theory description of the gravitational force. As a consequence, the gra…
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General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory is not fundamental though, but constitutes the lowest order term in an effective field theory description of the gravitational force. As a consequence, the gravitational dynamics should receive corrections by higher-derivative terms. This essay discusses structural aspects associated with these corrections and summarizes their imprint on static, spherically symmetric geometries. Along these lines, we critically reassess the common practice of using local field redefinitions in order to simplify the dynamics at the danger of shifting physics effects into sectors which are beyond the approximation under consideration.
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Submitted 25 July, 2024; v1 submitted 21 May, 2024;
originally announced May 2024.
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Leptogenesis, primordial gravitational waves, and PBH-induced reheating
Authors:
Basabendu Barman,
Suruj Jyoti Das,
Md Riajul Haque,
Yann Mambrini
Abstract:
We explore the possibility of producing the observed matter-antimatter asymmetry of the Universe uniquely from the evaporation of primordial black holes (PBH) that are formed in an inflaton-dominated background. Considering the inflaton $(φ)$ to oscillate in a monomial potential $V(φ)\proptoφ^n$, we show, it is possible to obtain the desired baryon asymmetry via vanilla leptogenesis from evaporati…
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We explore the possibility of producing the observed matter-antimatter asymmetry of the Universe uniquely from the evaporation of primordial black holes (PBH) that are formed in an inflaton-dominated background. Considering the inflaton $(φ)$ to oscillate in a monomial potential $V(φ)\proptoφ^n$, we show, it is possible to obtain the desired baryon asymmetry via vanilla leptogenesis from evaporating PBHs of initial mass $\lesssim 10$ g. We find that the allowed parameter space is heavily dependent on the shape of the inflaton potential during reheating (determined by the exponent of the potential $n$), the energy density of PBHs (determined by $β$), and the nature of the coupling between the inflaton and the Standard Model (SM). To complete the minimal gravitational framework, we also include in our analysis the gravitational leptogenesis set-up through inflaton scattering via exchange of graviton, which opens up an even larger window for PBH mass, depending on the background equation of state. We finally illustrate that such gravitational leptogenesis scenarios can be tested with upcoming gravitational wave (GW) detectors, courtesy of the blue-tilted primordial GW with inflationary origin, thus paving a way to probe a PBH-induced reheating together with leptogenesis.
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Submitted 1 August, 2024; v1 submitted 8 March, 2024;
originally announced March 2024.
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On the impact of perturbative counterterms on black holes
Authors:
Jesse Daas,
Cristobal Laporte,
Frank Saueressig
Abstract:
We determine the corrections to the Schwarzschild geometry arising from including the Goroff- Sagnotti counterterm in the gravitational dynamics. We find that static, asymptotically flat, and spherically symmetric geometries are completely characterized by their asymptotic mass and the coupling associated with the counterterm. The latter induces distinct corrections at sixth order of the parameter…
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We determine the corrections to the Schwarzschild geometry arising from including the Goroff- Sagnotti counterterm in the gravitational dynamics. We find that static, asymptotically flat, and spherically symmetric geometries are completely characterized by their asymptotic mass and the coupling associated with the counterterm. The latter induces distinct corrections at sixth order of the parameterized post-Newtonian expansion. The resulting spacetime geometries still exhibit an event horizon. In the parameter space accessible to numerical integration, the horizon area is smaller than its Schwarzschild counterpart, leading to an increase in the Hawking temperature. Corrections to the shadow size can be determined analytically and are used to give a first bound on the new coupling. While it is difficult to access the geometry inside of the event horizon, our analysis also provides evidence that the counterterm could resolve the curvature singularity appearing in the Schwarzschild geometry.
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Submitted 21 February, 2024; v1 submitted 27 November, 2023;
originally announced November 2023.
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Probing Quadratic Gravity with the Event Horizon Telescope
Authors:
Jesse Daas,
Kolja Kuijpers,
Frank Saueressig,
Michael F. Wondrak,
Heino Falcke
Abstract:
Quadratic gravity constitutes a prototypical example of a perturbatively renormalizable quantum theory of the gravitational interactions. In this work, we construct the associated phase space of static, spherically symmetric, and asymptotically flat spacetimes. It is found that the Schwarzschild geometry is embedded in a rich solution space comprising horizonless, naked singularities and wormhole…
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Quadratic gravity constitutes a prototypical example of a perturbatively renormalizable quantum theory of the gravitational interactions. In this work, we construct the associated phase space of static, spherically symmetric, and asymptotically flat spacetimes. It is found that the Schwarzschild geometry is embedded in a rich solution space comprising horizonless, naked singularities and wormhole solutions. Characteristically, the deformed solutions follow the Schwarzschild solution up outside of the photon sphere while they differ substantially close to the center of gravity. We then carry out an analytic analysis of observable signatures accessible to the Event Horizon Telescope, comprising the size of the black hole shadow as well as the radiation emitted by infalling matter. On this basis, we argue that it is the brightness within the shadow region which constrains the phase space of solutions. Our work constitutes the first step towards bounding the phase space of black hole type solutions with a clear quantum gravity interpretation based on observational data.
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Submitted 18 April, 2022;
originally announced April 2022.
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Asymptotically Safe Gravity-Fermion systems on curved backgrounds
Authors:
Jesse Daas,
Wouter Oosters,
Frank Saueressig,
Jian Wang
Abstract:
We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to $N_f$ Dirac fermions on maximally symmetric backgrounds. Based on Wetterich's equation we perform a detailed study of the resulting fixed point structure in a projection including the Einstein-Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermio…
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We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to $N_f$ Dirac fermions on maximally symmetric backgrounds. Based on Wetterich's equation we perform a detailed study of the resulting fixed point structure in a projection including the Einstein-Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term which breaks chiral symmetry explicitly. Our analysis identifies two infinite families of interacting RG fixed points which are viable candidates to provide a high-energy completion through the asymptotic safety mechanism. The fixed points exist for all values of $N_f$ outside of a small window situated at low values $N_f$ and become weakly coupled in the large $N_f$-limit. Symmetry-wise, they correspond to "quasi-chiral" and "non-chiral" fixed points. The former come with enhanced predictive power, fixing one of the couplings via the asymptotic safety condition. Moreover, the interplay of the fixed points allows for cross-overs from the non-chiral to the chiral fixed point, giving a dynamical mechanism for restoring the symmetry approximately at intermediate scales. Our discussion of chiral symmetry breaking effects provides strong indications that the topology of spacetime plays a crucial role when analyzing whether quantum gravity admits light chiral fermions.
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Submitted 2 July, 2021;
originally announced July 2021.
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Asymptotically Safe Gravity with Fermions
Authors:
Jesse Daas,
Wouter Oosters,
Frank Saueressig,
Jian Wang
Abstract:
We use the functional renormalization group equation for the effective average action to study the fixed point structure of gravity-fermion systems on a curved background spacetime. We approximate the effective average action by the Einstein-Hilbert action supplemented by a fermion kinetic term and a coupling of the fermion bilinears to the spacetime curvature. The latter interaction is singled ou…
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We use the functional renormalization group equation for the effective average action to study the fixed point structure of gravity-fermion systems on a curved background spacetime. We approximate the effective average action by the Einstein-Hilbert action supplemented by a fermion kinetic term and a coupling of the fermion bilinears to the spacetime curvature. The latter interaction is singled out based on a "smart truncation building principle". The resulting renormalization group flow possesses two families of interacting renormalization group fixed points extending to any number of fermions. The first family exhibits an upper bound on the number of fermions for which the fixed points could provide a phenomenologically interesting high-energy completion via the asymptotic safety mechanism. The second family comes without such a bound. The inclusion of the non-minimal gravity-matter interaction is crucial for discriminating the two families. Our work also clarifies the origin of the strong regulator-dependence of the fixed point structure reported in earlier literature and we comment on the relation of our findings to studies of the same system based on a vertex expansion of the effective average action around a flat background spacetime.
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Submitted 5 October, 2020; v1 submitted 25 May, 2020;
originally announced May 2020.
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Quasi-normal modes in a symmetric triangular barrier
Authors:
Poulami Dutta Roy,
Jagannath Das,
Sayan Kar
Abstract:
Quasi-normal modes (QNMs) of the massless scalar wave in $1+1$ dimensions are obtained for a symmetric, finite, triangular barrier potential. This problem is exactly solvable, with Airy functions involved in the solutions. Before obtaining the QNMs, we demonstrate how such a triangular barrier may arise in the context of scalar wave propagation in a tailor-made wormhole geometry. Thereafter, the F…
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Quasi-normal modes (QNMs) of the massless scalar wave in $1+1$ dimensions are obtained for a symmetric, finite, triangular barrier potential. This problem is exactly solvable, with Airy functions involved in the solutions. Before obtaining the QNMs, we demonstrate how such a triangular barrier may arise in the context of scalar wave propagation in a tailor-made wormhole geometry. Thereafter, the Ferrari-Mashhoon idea is used to show how bound states in a well potential may be used to find the QNMs in a corresponding barrier potential. The bound state condition in the exactly solvable triangular well and the transformed condition for finding the QNMs are written down. Real bound state energies and complex QNMs are found by solving the respective transcendental equations. Numerical integration of the wave equation yields the time domain profiles for scalar waves propagating in this wormhole geometry which illustrate the quasinormal ringing. Estimates relating the size of the wormhole throat (in units of solar mass) with the QNM frequencies are stated and discussed. Finally, we show how the effective potential and the QNMs for scalar perturbations of the Ellis--Bronnikov wormhole spacetime can be reasonably well--approximated using a properly parametrised triangular barrier.
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Submitted 18 October, 2019; v1 submitted 17 April, 2019;
originally announced April 2019.