We propose a triality relating the Double-Scaled SYK model, SL(2$\textit{,}$ ℂ) Chern-Simons theory on a disk with an irregular singularity at the center and the outcome of “real Schur quantization” applied to SU(2) Seiberg-Witten theory with Neumann boundary conditions. We give supporting evidence for our conjecture by establishing a precise match between a general class of correlators in all three systems.

Canada

Davide Gaiotto

United States

Herman Verlinde

SYK-Schur duality: double scaled SYK correlators from $$ \mathcal{N} $$ = 2 supersymmetric gauge theory

We introduce and study a candidate gravity dual to the double scaled SYK model in the form of an exactly soluble 2D de Sitter gravity model consisting of two spacelike Liouville CFTs with complex central charge adding up to $\textit{c}$ + $\textit{c}$ = 26. In [1] it was shown that the two-point function of physical operators in a doubled SYK model matches in the semi-classical limit with the Green’s function of a massive scalar field in 3D de Sitter space. As further evidence of the duality, we adapt a result from Zamolodchikov to compute the boundary two-point function of the 2D Liouville-de Sitter gravity model on a disk and find that it reproduces the exact DSSYK two-point function to all orders in $\textit{λ}$ = $\textit{p}$ $\textit{/N}$. We describe how the 2D Liouville-de Sitter gravity model arises from quantizing 3D de Sitter gravity.

Mengyang Zhang

SYK correlators from 2D Liouville-de Sitter gravity

We propose a new model of low dimensional de Sitter holography in the form of a pair of double-scaled SYK models at infinite temperature coupled via an equal energy constraint $\textit{H}$ = $\textit{H}$ . As a test of the duality, we compute the two-point function between two dressed SYK operators $$ {\mathcal{O}}_{\Delta } $$ that preserve the constraint. We find that in the large $\textit{N}$ limit, the two-point function precisely matches with the Green’s function of a massive scalar field of mass squared $\textit{m}$ = 4∆(1 – ∆) in a 3D de Sitter space-time with radius $\textit{R}$ /$\textit{G}$ = 4$\textit{πN}$/$\textit{p}$ . In this correspondence, the SYK time is identified with the proper time difference between the two operators. We introduce a candidate gravity dual of the doubled SYK model given by a JT/de Sitter gravity model obtained via a circle reduction from 3D Einstein-de Sitter gravity. We comment on the physical meaning of the finite de Sitter temperature and entropy.

Vladimir Narovlansky

Double-scaled SYK and de Sitter holography

We employ a probabilistic mesoscopic description to draw conceptual and quantitative analogies between Brownian motion and late-time fluctuations of thermal correlation functions in generic chaotic systems respecting ETH. In this framework, thermal correlation functions of ‘simple’ operators are described by stochastic processes, which are able to probe features of the microscopic theory only in a probabilistic sense. We apply this formalism to the case of semiclassical gravity in AdS , showing that wormhole contributions can be naturally identified as moments of stochastic processes. We also point out a ‘Matryoshka doll’ recursive structure in which information is hidden in higher and higher moments, and which can be naturally justified within the stochastic framework. We then re-interpret the gravitational results from the boundary perspective, promoting the OPE data of the CFT to probability distributions. The outcome of this study shows that semiclassical gravity in AdS can be naturally interpreted as a mesoscopic description of quantum gravity, and a mesoscopic holographic duality can be framed as a moment-vs.-probability-distribution duality.

Switzerland

Pietro Pelliconi

Julian Sonner

Gravity as a mesoscopic system

We use the Virasoro TQFT to derive an integral identity that we view as a non-rational generalization of the Verlinde formula for the Virasoro algebra with central charge $\textit{c}$ ≥ 25. The identity expresses the Virasoro fusion kernel as an integral over a ratio of modular S-kernels on the (punctured) torus. In particular, it shows that the one-point S-kernel diagonalizes the Virasoro 6$\textit{j}$ symbol. After carefully studying the analytic properties of this ‘Virasoro-Verlinde formula’, we present three applications. In boundary Liouville CFT, the formula ensures the open-closed duality of the boundary one-point function on the annulus. In pure 3d gravity, it provides an essential step in computing the partition function on hyperbolic 3-manifolds that fiber over the circle. Lastly, in AdS /CFT , the formula computes a three-boundary torus wormhole, which leads to a prediction for the statistical correlation between the density of states and two OPE coefficients in the dual large-$\textit{c}$ CFT ensemble. We conclude by discussing the implications of our result for the fusion rules in generic non-rational 2d CFTs.

Netherlands

Boris Post

France

Ioannis Tsiares

A non-rational Verlinde formula from Virasoro TQFT

We study the partition function of 3D de Sitter gravity defined as the trace over the Hilbert space obtained by quantizing the phase space of non-rotating Schwarzschild-de Sitter spacetime. Motivated by the correspondence with double scaled SYK, we identify the Hamiltonian with the gravitational Wilson-line that measures the conical deficit angle. We express the Hamiltonian in terms of canonical variables and find that it leads to the exact same chord rules and energy spectrum as the double scaled SYK model. We use the obtained match to compute the partition function and scalar two-point function in 3D de Sitter gravity.

Double-scaled SYK, chords and de Sitter gravity

Cardy-Verlinde (CV) formula relates the entropy of a strongly coupled conformal field theory (CFT) possessing AdS dual, at finite temperature, to its total energy (with an appropriate insertion of additional internal energy for charged systems) and Casimir energy. While the CV formula has been checked for various CFTs, in the present work, we intend to verify it directly, by exploiting a phenomenological matrix model, which is believed to qualitatively capture features of strongly coupled <math><mi>N</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> Super Yang-Mills theory on <math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math>, at finite temperature and chemical potential at large N.

India

Pavan Kumar Yerra

Chandrasekhar Bhamidipati

Sudipta Mukherji

Cardy-Verlinde formula from boundary matrix model

We remind the definition and main properties of the Krichever quasiclassical tau-function, and turn to the application of these formulas for recent studies of two-dimensional quantum gravity. We show, that in the case of minimal gravity it turns to be directly related with the Verlinde formula for minimal models, giving in particular case its one more direct proof. Generalizations for continuous “complex Liouville” theory are also briefly discussed.

Russia

A. Marshakov

On Krichever tau-function and Verlinde formula

We investigate the composite systems consisting of topological orders separated by gapped domain walls. We derive a pair of domain-wall Verlinde formulae, that elucidate the connection between the braiding of interdomain excitations labeled by pairs of anyons in different domains and quasiparticles in the gapped domain wall with their respective fusion rules. Through explicit non-Abelian examples, we showcase the calculation of such braiding and fusion, revealing that the fusion rules for interdomain excitations are generally fractional or irrational. By investigating the correspondence between composite systems and anyon condensation, we unveil the reason for designating these fusion rules as symmetry fractionalized (irrationalized) fusion rules. Our findings hold promise for applications across various fields, such as topological quantum computation, topological field theory, conformal field theory, and parton physics.

China

Yu Zhao

Hongyu Wang

Yuting Hu

Yidun Wan

Symmetry fractionalized (irrationalized) fusion rules and two domain-wall Verlinde formulae

In this study, charged AdS black holes with a string cloud are taken into consideration. We identify three distinct black hole solutions within a specific temperature range, which subsequently merge into a single black hole beyond this range in the case of spherical space with low chemical potential and string density. However, in the case of large chemical potential and string density, only one black hole solution exists for all temperatures. Notably, we observe that for flat and hyperbolic space, there is only one black hole solution irrespective of the chemical potential and string density. By subtracting the contribution of the extremal black hole from the on-shell Euclidean action, the thermodynamical quantities associated with these black holes are calculated. We also investigate the stability of these black holes and find that medium-sized black hole is unstable. In the dual boundary theory side we verify the existence of bound state of quark-antiquark pair. Finally, we establish the Cardy-Verlinde formula for the boundary theory and we observed an additional energy term arising because of the presence of string cloud.