JT gravity, KdV equations and macroscopic loop operators

Abstract

We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean $Ad{S}_2$ background using the matrix model description recently found by Saad, Shenker and Stanford [arXiv:1903.11115]. We show that the partition function of JT gravity is written as the expectation value of a macroscopic loop operator in the old matrix model of 2d gravity in the background where infinitely many couplings are turned on in a specific way. Based on this expression we develop a very efficient method of computing the partition function in the genus expansion as well as in the low temperature expansion by making use of the Korteweg-de Vries constraints obeyed by the partition function. We have computed both these expansions up to very high orders using this method. It turns out that we can take a low temperature limit with the ratio of the temperature and the genus counting parameter held fixed. We find the first few orders of the expansion of the free energy in a closed form in this scaling limit. We also study numerically the behavior of the eigenvalue density and the Baker-Akhiezer function using the results in the scaling limit.

44 pages, 6 figures, data of genus and low temperature expansions attached, v2: typos corrected, published version

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• Gravity factorized
• Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity
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• From Quantum Groups to Liouville and Dilaton Quantum Gravity
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• FZZT branes in JT gravity and topological gravity
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• Solving Puzzles in Deformed JT Gravity: Phase Transitions and Non-Perturbative Effects
• Alpha states demystified: Towards microscopic models of AdS${}_2$ holography
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• Differential identities for the structure function of some random matrix ensembles
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• Holographic complexity of Jackiw-Teitelboim gravity from Karch-Randall braneworld
• Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity
• Microstructure in matrix elements
• A Celestial Matrix Model
• $T\bar{T}$ deformation of random matrices
• Low-temperature entropy in JT gravity
• Deformations of JT Gravity via Topological Gravity and Applications
• Spectral form factor in the $\tau$-scaling limit
• Gravity without averaging
• The Schwarzian sector of higher spin CFTs
• Branes in JT (super)gravity from group theory
• Gravity as an ensemble and the moment problem
• $T\overline{T}$-deformed free energy of the Airy model
• Replica Wormholes from Liouville Theory
• Path integrals in JT gravity and Virasoro constraints
• Quantum Gravity Microstates from Fredholm Determinants
• Genus expansion of open free energy in 2d topological gravity
• Gravitational wavefunctions in JT supergravity
• A Black Hole Airy Tail
• KdV conformal symmetry breaking in nearly AdS${}_2$
• A proof of loop equations in 2d topological gravity
• Late time behavior of $n$-point spectral form factors in Airy and JT gravities
• Higher spin wormholes from modular bootstrap
• 't Hooft expansion of multi-boundary correlators in 2D topological gravity
• Quantum chaos in 2D gravity