We consider the algebra of observables of perturbative quantum gravity in the exterior of a stationary black hole or the static patch of de Sitter spacetime. It was previously argued in Refs. [1–3] that the backreaction of gravitons on the spacetime perturbs the area of the horizon at second order, which gives rise to a nontrivial constraint on the algebra of physical observables in the subregion. The corresponding “dressed” algebra including fluctuations of the total horizon area admits a well-defined trace and is type II. In this paper we show that, at the same perturbative order at which the horizon area (and angular momentum) fluctuates, gravitational backreaction also perturbs the horizon area in an angle-dependent way. These fluctuations are encoded in horizon charges—i.e., “edge modes”—which are related to an infinite dimensional “boost supertranslation” symmetry of the horizon. Together, these charges impose an infinite family of nontrivial constraints on the gravitational algebra. We construct the full algebra of observables which satisfies these constraints. We argue that the resulting algebra is type II and its trace is shown to take a universal form. The entropy of any “semiclassical state” is the generalized entropy with an additional edge mode contribution as well as a state-independent constant. For any black hole spacetime, the algebra has no maximum entropy state and is type <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>II</mi></mrow><mi>∞</mi></msub></math>. In de Sitter, the static patch is defined relative to the worldline of a localized “observer.” We show that a consistent quantization of the static-patch algebra requires a more realistic model of the observer, in which higher multipole moments perturb the “shape” of the cosmological horizon. We argue that a proper account of the observer’s rotational kinetic energy and (nongravitational) binding energy implies that the algebra is of type <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>II</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math> and thereby admits a maximum entropy state.

United States

Marc S. Klinger

Jonah Kudler-Flam

Gautam Satishchandran

Generalized black hole entropy is von Neumann entropy. II. The complete symmetry group and edge modes

We investigate the out-of-equilibrium dynamics of a relativistic <italic>Z</italic> <inf>2</inf>-symmetric scalar field theory with Langevin dynamics in two and three spatial dimensions under linear driving across magnetic first-order phase transitions, close to and far below the critical temperature <italic>T<inf>c</inf></italic>. Using classical-statistical lattice simulations, we find that if the driving timescale is sufficiently fast, the system exhibits finite-time scaling behavior independent of temperature and dimensionality, identical to that observed in mean-field simulations. In slow quenches near <italic>T<inf>c</inf></italic> this mean-field behavior crosses over to critical Kibble-Zurek scaling behavior, while for temperatures <italic>T</italic>&#8239;&#8810;&#8239; <italic>T<inf>c</inf></italic> nucleation and growth dominate the transition dynamics. Near the transition point where the order parameter changes sign, the crossover between mean-field and critical out-of-equilibrium dynamics is found to be well described by the leading algebraic correction to Kibble-Zurek scaling. We find that universal non-equilibrium scaling behavior can be observed for <italic>T</italic>&#8239;&#8818;&#8239; <italic>T<inf>c</inf></italic>, provided the driving is fast enough to avoid nucleation but slow enough for correlations to form, and compute the associated universal scaling functions for the order parameter.

Germany

Leon J. Sieke

Jessica Fuchs

Lorenz von Smekal

Non-equilibrium scaling across first-order transitions with self-interacting scalar fields

The standard parity-doublet model with its mass-mixing mechanism fails to describe the axial charge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>A</mi></msub></math> of the nucleon. While <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>A</mi></msub><mo>=</mo><mn>1</mn></math> in the original Gell-Mann–Levy model, which reproduces the Adler-Bell-Jackiw anomaly of QCD, in the presence of a chirally invariant baryon mass the mass mixing leads to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>A</mi></msub><mo>&lt;</mo><mn>1</mn></math>, whereas phenomenologically it is about 1.28. We propose to remedy this problem by introducing kinetic-mixing terms corresponding to meson-baryon derivative couplings, similar in spirit to the two-mixing-angle scenario of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>−</mo><msup><mi>η</mi><mo>′</mo></msup></math> mixing. This extended parity-doublet model contains five parameters in the effective baryonic Lagrangian. Three of them can be determined by using the empirical results for the axial charge of the nucleon together with the masses of the nucleon and its parity partner, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>N</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> resonance. We discuss various options of how to determine the remaining parameters, touching upon the mass of both parity partners if the chiral condensate is put to zero, the mass of the nucleon in the chiral limit, and the values of meson-baryon coupling constants related to the decays of the resonance to pion-nucleon and sigma-nucleon.

Cyprus

Christian Kummer

Sweden

Stefan Leupold

Kinetic mixing and axial charges in the parity-doublet model

We study modular theory in hyperfinite von Neumann algebras, i.e. in those of type II or type III, from the viewpoint of a subregion charge sector decomposition. We address this symmetry resolution by considering infinite tensor products of finite-dimensional algebras with fixed subregion charge values. An important ingredient is the combination of these algebras using direct integrals. This allows us to obtain the symmetry-resolved modular operator, modular flow, and modular correlation functions for hyperfinite algebras. Our approach establishes a mathematical foundation for recent results on symmetry resolution and modular theory in conformal field theory. Our analysis applies both to charges defined on a continuous range, or on a discrete set. The latter is of interest for condensed matter theory. Moreover, within the AdS/CFT correspondence we expect our findings to be relevant as a new ingredient for bulk spacetime reconstruction, including information from different boundary charge sectors.

Giuseppe Giulio

Moritz Dorband

Johanna Erdmenger

Henri Scheppach

Modular theory and symmetry resolution in hyperfinite von Neumann algebras

We investigate entanglement entropy between the pair of type II algebras of the double-scaled SYK (DSSYK) model given a chord state, its holographic interpretation as generalized horizon entropy; particularly in the (anti-)de Sitter ((A)dS) space limits of the bulk dual; and its connection with Krylov complexity. The density matrices in this formalism are operators in the algebras, which are specified by the choice of global state; and there exists a trace to evaluate their von Neumann entropy since the algebras are commutants of each other, which leads to a notion of algebraic entanglement entropy. We match it in triple-scaling limits to an area computed through a $\textit{Ryu-Takayanagi formula}$ in (A)dS space with entangling surfaces at the asymptotic timelike or spacelike boundaries respectively; providing a first-principles example of holographic entanglement entropy for (A)dS space. This result reproduces the Bekenstein-Hawking and Gibbons-Hawking entropy formulas for specific entangling regions points, while it decreases for others. This construction does not display some of the puzzling features in dS holography. The entanglement entropy remains real-valued since the theory is unitary, and it depends on the Krylov spread complexity of the Hartle-Hawking state.

Japan

Sergio Aguilar-Gutierrez

Cosmological entanglement entropy from the von Neumann algebra of double-scaled SYK & its connection with Krylov complexity

It has been argued that a finite effective temperature emerges and characterizes the thermal property of double-scaled SYK model in the infinite temperature limit [1]. Meanwhile, in the static patch of de Sitter, the maximally entangled state satisfies a KMS condition at infinite temperature [2], suggesting the Type II nature of the observable algebra gravitationally dressed to the observer. In this work, we analyze the double-scaled algebra generated by chord operators in the double-scaled SYK model and demonstrate that it exhibits features reflecting both perspectives. Specifically, we prove that the algebra is a Type II factor, and that the empty state with no chord satisfies the tracial property, in agreement with expectations from [3]. We further show that this state is cyclic and separating for the double-scaled algebra, based on which we explore its modular structure. We then explore various physical limits of the theory, drawing connections to JT gravity, the Hilbert space of baby universes, and Brownian double-scaled SYK. We also present analytic solutions to the energy spectrum in both the zero- and one-particle sectors of the left/right chord Hamiltonian.

Jiuci Xu

Von Neumann algebras in double-scaled SYK

We study the additivity and Haag duality of the von Neumann algebra of a quantum field theory $${\mathcal{T}}_{\mathcal{F}}$$ with 0-form (and the dual ($\textit{d}$ − 2)-form) (non)-invertible global symmetry $$\mathcal{F}$$ . We analyze the symmetric (uncharged) sector von Neumann algebra of $${\mathcal{T}}_{\mathcal{F}}$$ with the inclusion of bi-local and bi-twist operators in it. We establish the connection between the existence of these non-local operators in $${\mathcal{T}}_{\mathcal{F}}$$ and certain properties of the Lagrangian algebra $$\mathcal{L}$$ of the extended operators in the corresponding symmetry topological field theory (SymTFT). We prove that additivity or Haag duality of the symmetric sector von Neumann algebra is violated when $$\mathcal{L}$$ satisfies specific criteria, thus generalizing the result of Shao, Sorce and Srivastava to arbitrary dimensions. We further demonstrate the SymTFT construction via concrete examples in two dimensions.

South Korea

Qiang Jia

China

Jiahua Tian

Symmetry, symmetry topological field theory and von Neumann algebra

In this work we study the quark-meson model within a real-time formulation of the functional renormalization group (FRG) on the Schwinger-Keldysh contour. First, we discuss in detail the symmetry of thermal equilibrium for the fermionic sector of the Keldysh action. We take into account dissipation for the bosonic degrees of freedom in the spirit of the Caldeira-Leggett model by coupling the system to an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></math> invariant external heat bath. We study the effect of dissipation on static equilibrium properties, most prominently on the FRG flow of the effective potential and thus on the resulting phase diagram. We find that, unlike in classical systems, through the contributions from nonzero Matsubara modes the dissipative dynamics can in general have an effect on static observables. We investigate these effects within two phenomenological models for the temperature dependence of the pion damping to verify that they are quantitatively small. To estimate their largest possible influence, we consider limits where the damping constants approach infinity.

Johannes V. Roth

Yunxin Ye

Sören Schlichting

Effects of dissipation on phase diagram and bosonic excitations in the quark-meson model

QCD at nonzero isospin chemical potentials has phenomenological relevance for a series of physical systems and provides an ideal test ground for the modeling of dense, strongly interacting matter. The two-flavor quark-meson model is known to effectively describe the condensation of charged pions in QCD that occurs in this setting. In this paper, we derive a renormalization group invariant mean-field formulation of the model and demonstrate that the resulting phase diagram and equation of state are in quantitative agreement with data from lattice QCD simulations at small and intermediate isospin chemical potentials. In particular, the speed of sound from the model shows an excess over the conformal bound, as previously seen in lattice computations, in agreement with chiral perturbation theory. We then consider the speed of sound in the limit of large isospin chemical potentials and see that it approaches the conformal limit from above, in qualitative agreement with recent lattice results and in quantitative agreement with perturbation theory in the presence of a Bardeen-Cooper-Schrieffer gap. Finally, we consider the phase diagram in the approach to the chiral limit. We find that within the model, the chiral phase transition connects to the pion condensation phase boundary in the chiral limit and we discuss the implications for the properties of the chiral transition point.

Bastian B. Brandt

Volodymyr Chelnokov

Hungary

Gergely Endrődi

Gergely Markó

Daniel Scheid

Renormalization group invariant mean-field model for QCD at finite isospin density

We use a novel real-time formulation of the functional renormalization group (FRG) for dynamical systems with reversible mode couplings to study model H, the conjectured dynamic universality class of the quantum chromodynamics (QCD) critical point. We emphasize the structural similarities with model G, conjectured to be the dynamic universality class of the chiral phase transition in the limit of two massless quark flavors. Importantly, our formulation of the real-time FRG preserves all relevant symmetries throughout the FRG flow which, e.g., guarantees the nonrenormalization of the reversible mode couplings, as but one exact result. We derive nonperturbative RG flow equations for the kinetic coefficients of both, model G and H, in parallel, and discuss commonalities and differences in the resulting fixed-point structure and dynamic critical exponents, such as weak-scaling relations which hold in either case versus the characteristic strong scaling of model G which is absent in model H.

Universal critical dynamics near the chiral phase transition and the QCD critical point