TQFT gravity and ensemble holography
arXiv:2405.20366 · doi:10.1007/JHEP02(2025)091
Abstract
We outline a general derivation of holographic duality between "TQFT gravity" - the path integral of a 3d TQFT summed over different topologies - and an ensemble of boundary 2d CFTs. The key idea is to place the boundary ensemble on a Riemann surface of very high genus, where the duality trivializes. The duality relation at finite genus is then obtained by genus reduction. Our derivation is generic and does not rely on an explicit form of the bulk or boundary partition functions. It guarantees unitarity and suggests that the bulk sum should include all possible topologies. In the case of Abelian Chern-Simons theory with compact gauge group we show that the weights of the boundary ensemble are equal, while the bulk sum reduces to a finite sum over equivalence classes of topologies, represented by handlebodies with possible line defects.
30 pages, 2 figures; v2 journal version
References in corpus (40)
- Symmetries and Strings in Field Theory and Gravity
- Quantum Gravity Partition Functions in Three Dimensions
- Non-Invertible Duality Defects in 3+1 Dimensions
- Higher Gauging and Non-invertible Condensation Defects
- Orbifold groupoids
- One-loop Partition Functions of 3D Gravity
- Topological boundary conditions in abelian Chern-Simons theory
- AdS gravity and random CFT
- The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral
- Averaging Over Narain Moduli Space
- Free partition functions and an averaged holographic duality
- Poincare Series, 3D Gravity and CFT Spectroscopy
- Semiclassical 3D gravity as an average of large-c CFTs
- Partition functions and elliptic genera from supergravity
- The Gravity Dual of the Ising Model
- Solving 3d Gravity with Virasoro TQFT
- The Virasoro Minimal String
- Bootstrapping Non-Invertible Symmetries
- Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants
- Entanglement Entropy and the Colored Jones Polynomial
- Narain to Narnia
- Adding Flavor to the Narain Ensemble
- Comments on the holographic description of Narain theories
- Chern-Simons Invariants from Ensemble Averages
- AdS wormholes from a modular bootstrap
- Entanglement from Topology in Chern-Simons Theory
- Chern-Simons Gauge Theory and the AdS(3)/CFT(2) Correspondence
- Poincaré Series, 3d Gravity and Averages of Rational CFT
- 3d gravity from Virasoro TQFT: Holography, wormholes and knots
- Teichmuller TQFT vs Chern-Simons Theory
- Narain CFTs and error-correcting codes on finite fields
- Narain CFTs and Quantum Codes at Higher Genus
- Multiboundary wormholes and OPE statistics
- Classical Codes and Chiral CFTs at Higher Genus
- From Topological to Quantum Entanglement
- Establishing strongly-coupled 3D AdS quantum gravity with Ising dual using all-genus partition functions
- Holographic description of Narain CFTs and their code-based ensembles
- AdS Gravity and RCFT Ensembles with Multiple Invariants
- Entanglement Classification from a Topological Perspective
- Wormholes and surface defects in rational ensemble holography