We study the thermal partition function of Jackiw-Teitelboim (JT)
gravity using the matrix model description recently found by Saad,
Shenker and Stanford. 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 also generalize our analysis to the case of multi-boundary
correlators with the help of the boundary creation operator. 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 arises.
This talk is based on the work with Kazuhiro Sakai (arXiv:1911.01659,arXiv:2004.07555)