Solving Puzzles in Deformed JT Gravity: Phase Transitions and Non-Perturbative Effects

TL;DR

This paper investigates phase transitions and non-perturbative effects in deformed JT gravity models, revealing conditions for consistency and the role of multi-valued solutions in the matrix model description.

Contribution

It identifies the source of unitarity issues in deformed JT gravity and proposes phase transition resolutions, advancing understanding of non-perturbative effects in these models.

Findings

Certain deformations exhibit phase transitions that resolve unitarity problems.

Some deformations are shown to be perturbatively and non-perturbatively inconsistent.

Qualitative agreement with semi-classical black hole phase structure is observed.

Abstract

Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.