Liouville quantum gravity -- holography, JT and matrices

Abstract

We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of $SL(2,\mathbb{R})$, a connection we develop in some detail. For the case of the $(2,p)$ minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large $p$ limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large $p$ limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a $\sinh \Phi$ dilaton potential.

77 pages, v5: corrected equations (7.46) and (7.48)

References in corpus (12)

• An Investigation of AdS${}_2$ Backreaction and Holography
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• JT gravity, KdV equations and macroscopic loop operators
• On Correlation Numbers in 2D Minimal Gravity and Matrix Models
• Wormhole calculus, replicas, and entropies
• A CFT Perspective on Gravitational Dressing and Bulk Locality
• The double scaled limit of Super--Symmetric SYK models
• Liouville theory and Matrix models: A Wheeler DeWitt perspective
• Boundary correlation numbers in one matrix model
• Boundary operators in minimal Liouville gravity and matrix models

Cited by in corpus (68)

• Quantum chaos and the complexity of spread of states
• Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity
• Late time physics of holographic quantum chaos
• Summing over Geometries in String Theory
• The Virasoro Minimal String
• Gravity factorized
• Classifying boundary conditions in JT gravity: from energy-branes to $\alpha$-branes
• String correlators on ${\text{AdS}}_3$: Three-point functions
• A proposal for 3d quantum gravity and its bulk factorization
• An effective matrix model for dynamical end of the world branes in Jackiw-Teitelboim gravity
• Dynamical actions and q-representation theory for double-scaled SYK
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• An integrable road to a perturbative plateau
• FZZT branes in JT gravity and topological gravity
• Interacting systems and wormholes
• A JT supergravity as a double-cut matrix model
• A universe field theory for JT gravity
• Solving Puzzles in Deformed JT Gravity: Phase Transitions and Non-Perturbative Effects
• Supergroup Structure of Jackiw-Teitelboim Supergravity
• Correlators of double scaled SYK at one-loop
• JT Gravity Limit of Liouville CFT and Matrix Model
• Degenerate operators in JT and Liouville (super)gravity
• The dilaton gravity hologram of double-scaled SYK
• Wormholes, branes and finite matrices in sine dilaton gravity
• Comments on the Quantum Field Theory of the Coulomb Gas Formalism
• dS${}_2$ Supergravity
• Microstructure in matrix elements
• Supersymmetric Virasoro Minimal Strings
• Quantum exponentials for the modular double and applications in gravity models
• 3d Gravity as a random ensemble
• Hartle-Hawking state and its factorization in 3d gravity
• Dynamical symmetries of homogeneous minisuperspace models
• Deformations of JT Gravity via Topological Gravity and Applications
• Phase transitions for deformations of JT supergravity and matrix models
• Gravity without averaging
• dS${}_2$ as excitation of AdS${}_2$
• Branes in JT (super)gravity from group theory
• The complex Liouville string: worldsheet boundaries and non-perturbative effects
• Ensemble averages, Poisson processes and Microstates
• The complex Liouville string: the gravitational path integral
• Path integrals in JT gravity and Virasoro constraints
• Replica Wormholes from Liouville Theory
• Disc partition function of 2d $R^2$ gravity from DWG matrix model
• Quantum Groups as Global Symmetries
• Multiway Junction Conditions: Booklets and Webs
• Quantum group origins of edge states in double-scaled SYK
• Baby universes in 2d and 4d theories of quantum gravity
• The two-sphere partition function in two-dimensional quantum gravity at fixed area
• Gravitational wavefunctions in JT supergravity
• Les Houches lectures on two-dimensional gravity and holography
• Retrieving black hole information from the main Lorentzian saddle point
• Encoded information of mixed correlations: the views from one dimension higher
• Lifshitz tails at spectral edge and holography with a finite cutoff
• $x-y$ swap for $(2,2p+1)$ minimal string
• A proof of loop equations in 2d topological gravity
• Chaos and moduli space volumes in unorientable JT gravity
• Fermions, quantum gravity and holography in two dimensions
• Boundary Conditions for $\mathrm{Ad}{\mathrm{S}}_2$ Dilaton Gravity
• Holographic JT gravity with quartic couplings
• Higher spin wormholes from modular bootstrap
• Probing sine dilaton gravity with flow central charge
• A so(2,2) extension of JT gravity via the Virasoro-Kac-Moody semidirect product
• Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions
• Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics
• Classical gravitational anomalies of Liouville theory
• Asymptotics of Weil-Petersson volumes and two-dimensional quantum gravities
• Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics
• Fiducial observers and the thermal atmosphere in the black hole quantum throat