Les Houches lectures on two-dimensional gravity and holography

Abstract

Lecture notes prepared for the Les Houches school "Quantum Geometry: Mathematical Methods for Gravity, Gauge Theories and Non-Perturbative Physics" that took place during the summer 2024. We cover the techniques to perform the exact gravitational path integral of two-dimensional dilaton-gravity, and supergravity, over spacetimes with arbitrary topology, with an application to black holes. We discuss the connection with random matrix models and moduli spaces of hyperbolic surfaces briefly, since those concepts were covered in other lectures of the school.

55 pages; v2: typo corrected in section 4.4

References in corpus (88)

• Eternal Black Holes in AdS
• The entropy of Hawking radiation
• Chaos in AdS${}_2$ holography
• An Investigation of AdS${}_2$ Backreaction and Holography
• Black Holes and Random Matrices
• Bekenstein-Hawking Entropy and Strange Metals
• Dilaton Gravity in Two Dimensions
• Holographic metals and the fractionalized Fermi liquid
• Fermionic Localization of the Schwarzian Theory
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Solving the Schwarzian via the Conformal Bootstrap
• Eternal traversable wormhole
• A semiclassical ramp in SYK and in gravity
• Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity
• The Quantum Gravity Dynamics of Near Extremal Black Holes
• On the Dynamics of Near-Extremal Black Holes
• AdS${}_3$ gravity and random CFT
• The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral
• De-singularization by rotation
• Statistical mechanics of a two-dimensional black hole
• Low-dimensional de Sitter quantum gravity
• The Schwarzian Theory - A Wilson Line Perspective
• An exact quantization of Jackiw-Teitelboim gravity
• A universal Schwarzian sector in two-dimensional conformal field theories
• Liouville quantum gravity -- holography, JT and matrices
• Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models
• 5D Rotating Black Holes and the nAdS${}_2$/nCFT${}_1$ Correspondence
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• Defects in Jackiw-Teitelboim Quantum Gravity
• Conformal Symmetry Breaking and Thermodynamics of Near-Extremal Black Holes
• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• Developments in Topological Gravity
• Menagerie of AdS${}_2$ boundary conditions
• Extremal and Near-Extremal Black Holes and Near-$CF{T}_1$
• Nearly AdS2 Sugra and the Super-Schwarzian
• Explorations of Non-Perturbative JT Gravity and Supergravity
• The Virasoro Minimal String
• Eigenbranes in Jackiw-Teitelboim gravity
• Dilaton-gravity, deformations of the minimal string, and matrix models
• JT Supergravity, Minimal Strings, and Matrix Models
• Gravity factorized
• Looking at supersymmetric black holes for a very long time
• Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space
• A new cohomology class on the moduli space of curves
• Holography for people with no time
• Matrix Models and Deformations of JT Gravity
• Logarithmic Corrections to Kerr Thermodynamics
• An integrable road to a perturbative plateau
• Towards the Holographic Dual of N = 2 SYK
• A JT supergravity as a double-cut matrix model
• Solving Puzzles in Deformed JT Gravity: Phase Transitions and Non-Perturbative Effects
• Two dimensional Nearly de Sitter gravity
• BPS Chaos
• JT gravity with matter, generalized ETH, and Random Matrices
• Phases of $\mathcal{N}=2$ Sachdev-Ye-Kitaev models
• The statistical mechanics of near-BPS black holes
• Quantum exponentials for the modular double and applications in gravity models
• Thermodynamics of Near-Extreme Black Holes
• $N=2$ JT Supergravity and Matrix Models
• Gravity without averaging
• Phase transitions for deformations of JT supergravity and matrix models
• Non-Perturbative Random Matrix Model of $\mathcal{N}=2$ JT Supergravity
• The complex Liouville string
• Generalizations of McShane's identity to hyperbolic cone-surfaces
• Quantum Gravity Microstates from Fredholm Determinants
• Weil-Petersson volumes and cone surfaces
• Matrix models for eigenstate thermalization
• New insights on near-extremal black holes
• A convergent genus expansion for the plateau
• Characters, Coadjoint Orbits and Duistermaat-Heckman Integrals
• Les Houches lecture notes on topological recursion
• Spin-Statistics for Black Hole Microstates
• 2D dilaton gravity and the Weil-Petersson volumes with conical defects
• God of the Gaps: Random matrix models and the black hole spectral gap
• The evaporation of charged black holes
• A natural basis for intersection numbers
• Firewalls from wormholes
• On the non-perturbative bulk Hilbert space of JT gravity
• Thermodynamics of the near-extremal Kerr spacetime
• Mixed 't Hooft Anomalies and the Witten Effect for AdS Black Holes
• Les Houches lecture notes on moduli spaces of Riemann surfaces
• A Mirzakhani recursion for non-orientable surfaces
• Firewalls at exponentially late times
• Looking at extremal black holes from very far away
• Lengths of geodesics on non-orientable hyperbolic surfaces
• Semi-classical dilaton gravity and the very blunt defect expansion
• Supersymmetry breaking in SYK and the black hole spectrum
• The spectrum of near-BPS Kerr-Newman black holes and the ABJM mass gap

Cited by in corpus (2)

• Massive fields and Wilson spools in JT gravity
• Les Houches lecture notes on moduli spaces of Riemann surfaces