Abstract
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.
Highlights
The random matrix model which arises in the topological recursion of the Weil-Petersson volume [16]
We found that in the low temperature regime the genus expansion can be reorganized in the following scaling limit, which we call the ’t Hooft limit
We find the analytic form of the spectral form factor (SFF) in the ’t Hooft limit and show that the SFF in JT gravity exhibits the characteristic feature of the so-called ramp and plateau, as expected for a chaotic system with random matrix statistics of eigenvalues
Summary
In this paper we will generalize our method [12] developed for one-boundary partition function to the case of multi-boundary correlators. As we showed in [12], JT gravity can be regarded as a special case of the general Witten-Kontsevich topological gravity [17, 18]. In this model the intersection numbers κ τd1 · · · τdn g,n =. We can define a natural deformation of JT gravity by (partially) releasing tk from the constraint tk = γk and regard them as deformation parameters. This is one of our main ideas in [12] and enables us to investigate JT gravity using the techniques of the traditional 2d gravity.
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