Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
arXiv:2403.03179 · doi:10.21468/SciPostPhys.19.6.163
Abstract
We demonstrate that, by utilizing the boundary conformal field theory (BCFT) operator algebra of the Liouville CFT, one can express its path-integral on any Riemann surface as a three dimensional path-integral with appropriate boundary conditions, generalising the recipe for rational CFTs \cite{Hung:2019bnq, Brehm:2021wev, Chen:2022wvy, Cheng:2023kxh}. This serves as a constructive method for deriving the \textit{quantum} holographic dual of the CFT, which reduces to Einstein gravity in the large central charge limit. As a byproduct, the framework provides an explicit discrete state-sum of a 3D non-chiral topological theory constructed from quantum symbols of with non-trivial boundary conditions, representing a long-sought non-perturbative discrete formulation of 3D pure gravity with negative cosmological constant, at least within a class of three manifolds. This constitutes the first example of an exact holographic tensor network that reproduces a known irrational CFT with a precise quantum gravitational interpretation.
16 pages + appendices, 12 figures; v2 typos corrected and references added; v3: references added; discussion of difficulties in earlier works and their connection to the present work included; expanded discussion on RG and wavefunction tensor networks added; v4: Published version in SciPost Physics
References in corpus (42)
- Generalized Global Symmetries
- On space of integrable quantum field theories
- Tensor renormalization group approach to 2D classical lattice models
- Duality and defects in rational conformal field theory
- Entanglement Entropy at Large Central Charge
- Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
- The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
- Semiclassical 3D gravity as an average of large-c CFTs
- The Ponzano-Regge model
- Topological Defects on the Lattice: Dualities and Degeneracies
- Holographic Holes in Higher Dimensions
- Consistency Conditions for an AdS/MERA Correspondence
- Exact entanglement renormalization for string-net models
- Solving 3d Gravity with Virasoro TQFT
- From Path Integrals to Tensor Networks for AdS/CFT
- A CFT Perspective on Gravitational Dressing and Bulk Locality
- A proposal for 3d quantum gravity and its bulk factorization
- Topological symmetry in quantum field theory
- Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
- Simulating Holographic Conformal Field Theories on Hyperbolic Lattices
- 3d gravity from Virasoro TQFT: Holography, wormholes and knots
- Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography
- Toward random tensor networks and holographic codes in CFT
- Holographic Tensor Networks in Full AdS/CFT
- The black hole interior from non-isometric codes and complexity
- A note on the bulk interpretation of the Quantum Extremal Surface formula
- 6j symbols for U_q(sl_2) and non-Euclidean tetrahedra
- Holographic Tensor Networks with Bulk Gauge Symmetries
- Hartle-Hawking state and its factorization in 3d gravity
- Semiclassical Gravity from Averaged Boundaries in two-dimensional BCFTs
- Multipartite edge modes and tensor networks
- Notes on crossing transformations of Virasoro conformal blocks
- Background independent tensor networks
- The infinite-dimensional HaPPY code: entanglement wedge reconstruction and dynamics
- Conformal Turaev-Viro Theory
- Lattice models from CFT on surfaces with holes I: Torus partition function via two lattice cells
- Triangulating quantum gravity in AdS
- A new look at the entanglement entropy of a single interval in a 2d CFT
- Turaev-Viro invariant from the modular double of
- QG from SymQRG: AdS/CFT Correspondence as Topological Symmetry-Preserving Quantum RG Flow
- On the Quantum Information Content of a Hawking Pair
- Asymptotics of - symbols and anti-de Sitter tetrahedra