Matching partition functions of deformed JT gravity and the cSYK model

TL;DR

This paper constructs a deformed JT gravity model that replicates the thermodynamics and chaos properties of the large-q cSYK model, establishing a concrete gravitational dual.

Contribution

It derives a specific deformed JT gravity Lagrangian matching the cSYK model's partition function and chaos characteristics, advancing the understanding of their duality.

Findings

Matching partition functions and equations of state.

Overlap of Lyapunov exponents near phase transition.

Open questions about Lyapunov exponents at low temperatures.

Abstract

Motivated by recent analogies between the large-$q$ cSYK model and charged black holes, we aim to find a concrete gravitation theory with a matching partition function. Our main focus is to match the thermodynamics of the $(0+1)$-dimensional cSYK model, with that of a $(1+1)$-dimensional gravitational model. We focus on a model of deformed JT gravity, characterized by some unknown dilaton potential function and unknown dilaton-to-Maxwell field coupling. By finding the general solutions, we are able to find the Lagrangian which produces the same partition function and equation of state as that of the considered SYK model. We go beyond showing that the thermodynamics overlaps, by also showing that the Lyapunov exponents, characterizing the degree of chaos, overlap close to the second order phase transition. In the low temperature rescaled regime, there remains open questions about the Lyapunov exponents, given that our analysis ignores the black hole back action which can be large in this regime.