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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.
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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 order by directly solving the Korteweg-De Vries equation. We first explain how to compute the t Hooft expansion of the one-boundary correlator. The algorithm is very similar to that for the genus expansion of the open free energy. We next show that the t Hooft expansion of correlators with more than one boundary can be computed algebraically from the correlators with a lower number of boundaries. We explicitly compute the t Hooft expansion of the $n$-boundary correlators for $n=1,2,3$. Our results reproduce previously obtained results for Jackiw-Teitelboim gravity and also the t Hooft expansion of the exact result of the three-boundary correlator which we calculate independently in the Airy case.
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, we reproduce the Schwarzian semiclassical expansion beyond leading order. The computation is done for arbitrary temperature and finite boundary distances, in the case of disk and trumpet topologies. A formula presenting the perturbative result (for $lambda in mathbb{N}/2$) at any given order in terms of generalized Apostol-Bernoulli polynomials is also obtained. The limit of zero temperature is then considered, obtaining a compact expression that allows to discuss the asymptotic behaviour of the perturbative series. Finally we highlight the possibility to express the exact result as particular combinations of Mordell integrals.
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 that they cured by procedures that render the physics non-unique. This might not be a desirable property for a system that is supposed to capture key features of quantum black holes. Presented here is a model with identical perturbative physics at high energy that instead has a stable and unambiguous non-perturbative completion of the physics at low energy. An explicit examination of the full spectral density function shows how this is achieved. The new model, which is based on complex matrix models, also allows for the straightforward inclusion of spacetime features analogous to Ramond-Ramond fluxes. Intriguingly, there is a deformation parameter that connects this non-perturbative formulation of JT gravity to one which, at low energy, has features of a super JT gravity.
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-Zirnbauer ensembles. JT gravity has been shown to be dual to the double-scaling limit of a $beta =2$ ensemble, with a classical eigenvalue density $propto e^{S_0}sqrt{E}$ when $0 < E ll 1$. We use universal results about the distribution of the smallest eigenvalues in such ensembles to calculate $kappa$ up to corrections that we argue are doubly exponentially small in $S_0$.
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, we discuss the counting of the degrees of freedom for some specific classes of multi-gravity potentials, and unveil connections among a variety of apparently different models. Quantization of multi-gravity models can be then achieved from both the Hartle-Hawking no-boundary proposal, the SYK partition function and the spin-foam approaches. We comment on the SYK quantization procedure, and deepen in the appendix the quantization scheme naturally achieved in the $BF$ framework. The new multi-gravity theory hence recovered presents intriguing applications for analogue gravitational models developed for condensed matter physics, including graphene, endowed with defects and high intensity magnetic fields.
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