Establishing strongly-coupled 3D AdS quantum gravity with Ising dual using all-genus partition functions

Abstract

We study 3D pure Einstein quantum gravity with negative cosmological constant, in the regime where the AdS radius $l$ is of the order of the Planck scale. Specifically, when the Brown-Henneaux central charge $c=3l/2G_N$ ($G_N$ is the 3D Newton constant) equals $c=1/2$, we establish duality between 3D gravity and 2D Ising conformal field theory by matching gravity and conformal field theory partition functions for AdS spacetimes with general asymptotic boundaries. This duality was suggested by a genus-one calculation of Castro et al. [Phys. Rev. D {\bf 85}, 024032 (2012)]. Extension beyond genus-one requires new mathematical results based on 3D Topological Quantum Field Theory; these turn out to uniquely select the $c=1/2$ theory among all those with $c<1$, extending the previous results of Castro et al.. Previous work suggests the reduction of the calculation of the gravity partition function to a problem of summation over the orbits of the mapping class group action on a "vacuum seed". But whether or not the summation is well-defined for the general case was unknown before this work. Amongst all theories with Brown-Henneaux central charge $c<1$, the sum is finite and unique {\it only} when $c=1/2$, corresponding to a dual Ising conformal field theory on the asymptotic boundary.

arXiv comment54 pages, 12 figures

References in corpus (32)

• Anyons in an exactly solved model and beyond
• The Black Hole in Three Dimensional Space Time
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Black Hole Entropy from Near-Horizon Microstates
• AdS3 Black Holes and a Stringy Exclusion Principle
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Quantum Gravity Partition Functions in Three Dimensions
• An AdS_3 Dual for Minimal Model CFTs
• One-loop Partition Functions of 3D Gravity
• What We Don't Know about BTZ Black Hole Entropy
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Black Holes and Wormholes in 2+1 Dimensions
• Multiboundary Wormholes and Holographic Entanglement
• The two-eigenvalue problem and density of Jones representation of braid groups
• A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
• Holography and wormholes in 2+1 dimensions
• The kernel of the modular representation and the Galois action in RCFT
• On Rényi entropies of disjoint intervals in conformal field theory
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• Congruence Subgroups and Generalized Frobenius-Schur Indicators
• The Gravity Dual of the Ising Model
• Rational Conformal Field Theories and Complex Multiplication
• Bekenstein-Hawking Entropy as Topological Entanglement Entropy
• On Non-handlebody Instantons in 3D Gravity
• Holographic partition functions and phases for higher genus Riemann surfaces
• Analytic Continuation for Asymptotically AdS 3D Gravity
• Geometrical Finiteness, Holography, and the BTZ Black Hole
• On classification of extremal non-holomorphic conformal field theories
• Congruence Subgroups and Super-Modular Categories
• Topological Entanglement Entropy in Euclidean AdS3 via Surgery
• On Topological Quantum Computing With Mapping Class Group Representations

Cited by in corpus (14)

• Averaging Over Narain Moduli Space
• Free partition functions and an averaged holographic duality
• Partition functions of the tensionless string
• Wormholes and Spectral Statistics in the Narain Ensemble
• Poincaré Series, 3d Gravity and Averages of Rational CFT
• Averaging over moduli in deformed WZW models
• Narain CFTs and Quantum Codes at Higher Genus
• Discreteness and Integrality in Conformal Field Theory
• AdS${}_3$ Gravity and RCFT Ensembles with Multiple Invariants
• TQFT gravity and ensemble holography
• Conical spaces, modular invariance and $c_{p,1}$ holography
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Holographic duality for Ising CFT with boundary
• A universal sum over topologies in 3d gravity