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We continue the systematic study of the thermal partition function of Jackiw-Teitelboim (JT) gravity started in [arXiv:1911.01659]. We generalize our analysis to the case of multi-boundary correlators with the help of the boundary creation operator. We clarify how the Korteweg-de Vries constraints arise in the presence of multiple boundaries, deriving differential equations obeyed by the correlators. The differential equations allow us to compute the genus expansion of the correlators up to any order without ambiguity. We also formulate a systematic method of calculating the WKB expansion of the Baker-Akhiezer function and the t Hooft expansion of the multi-boundary correlators. This new formalism is much more efficient than our previous method based on the topological recursion. We further investigate the low temperature expansion of the two-boundary correlator. We formulate a method of computing it up to any order and also find a universal form of the two-boundary correlator in terms of the error function. Using this result we are able to write down the analytic form of the spectral form factor in JT gravity and show how the ramp and plateau behavior comes about. We also study the Hartle-Hawking state in the free boson/fermion representation of the tau-function and discuss how it should be related to the multi-boundary correlators.
We study multi-boundary correlators of Witten-Kontsevich topological gravity in two dimensions. We present a method of computing an open string like expansion, which we call the t Hooft expansion, of the $n$-boundary correlator for any $n$ up to any
We study the perturbative series associated to bi-local correlators in Jackiw-Teitelboim (JT) gravity, for positive weight $lambda$ of the matter CFT operators. Starting from the known exact expression, derived by CFT and gauge theoretical methods, w
Recently, Saad, Shenker and Stanford showed how to define the genus expansion of Jackiw-Teitelboim quantum gravity in terms of a double-scaled Hermitian matrix model. However, the models non-perturbative sector has fatal instabilities at low energy t
For ensembles of Hamiltonians that fall under the Dyson classification of random matrices with $beta in {1,2,4}$, the low-temperature mean entropy can be shown to vanish as $langle S(T)ranglesim kappa T^{beta+1}$. A similar relation holds for Altland
We study a series of powerful correspondences among new multi-gravity extensions of the Jackiw-Teitelboim model, multi-SYK models and multi-Schwarzian quantum mechanics, in the $rm{(A)dS_{2}/CFT}$ arena. Deploying a $BF$-like formulation of the model