JT supergravity and Brezin-Gross-Witten tau-function

Abstract

We study thermal correlation functions of Jackiw-Teitelboim (JT) supergravity. We focus on the case of JT supergravity on orientable surfaces without time-reversal symmetry. As shown by Stanford and Witten recently, the path integral amounts to the computation of the volume of the moduli space of super Riemann surfaces, which is characterized by the Brezin-Gross-Witten (BGW) tau-function of the KdV hierarchy. We find that the matrix model of JT supergravity is a special case of the BGW model with infinite number of couplings turned on in a specific way, by analogy with the relation between bosonic JT gravity and the Kontsevich-Witten (KW) model. We compute the genus expansion of the one-point function of JT supergravity and study its low-temperature behavior. In particular, we propose a non-perturbative completion of the one-point function in the Bessel case where all couplings in the BGW model are set to zero. We also investigate the free energy and correlators when the Ramond-Ramond flux is large. We find that by defining a suitable basis higher genus free energies are written exactly in the same form as those of the KW model, up to the constant terms coming from the volume of the unitary group. This implies that the constitutive relation of the KW model is universal to the tau-function of the KdV hierarchy.

arXiv comment36 pages, v2: typos corrected, footnotes and references added, v3: several explanations added, typos corrected, published version

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• $T\bar{T}$ deformation of random matrices
• Deformations of JT Gravity via Topological Gravity and Applications
• Genus expansion of open free energy in 2d topological gravity
• Cut-and-join operators for higher Weil-Petersson volumes
• A proof of loop equations in 2d topological gravity
• Discrete JT gravity as an Ising model
• 't Hooft expansion of multi-boundary correlators in 2D topological gravity
• Quantum chaos in 2D gravity
• Asymptotics of Weil-Petersson volumes and two-dimensional quantum gravities