JT gravity, KdV equations and macroscopic loop operators
Nov 5, 2019Citations per year
Abstract: (Springer)
We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean AdS 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.Note:
- 44 pages, 6 figures, data of genus and low temperature expansions attached, v2: typos corrected, published version
- 2D Gravity
- Matrix Models
- Integrable Hierarchies
- partition function: thermal
- temperature: ratio
- temperature: low
- gravitation
- matrix model
- background
- scaling
References(64)
Figures(6)
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