Abstract
We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean AdS2 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.
Highlights
We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean AdS2 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
Summary
We will show that JT gravity is realized as the conventional 2d topological gravity in the background where infinitely many couplings are turned on in a specific way. We will consider the partition function of JT gravity on Riemann surfaces with one boundary and introduce its two-parameter generalization. Function is closely related to the tau-function for the KdV hierarchy. Using this relation we will derive a simple differential equation which uniquely determines the partition function both in the genus and the low temperature expansions
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