$T\bar{T}$ deformation of random matrices

TL;DR

This paper explores the $T\bar{T}$ deformation of random matrix models, revealing phase transitions and spectral complexification, with implications for quantum gravity and gauge theories.

Contribution

It provides a consistent definition of the $T\bar{T}$ deformation for random matrices, including both perturbative and non-perturbative solutions, and analyzes phase transitions.

Findings

Deformed models exhibit a phase transition at a critical coupling.

The transition involves a change from single to double-cut spectrum, similar to the Gross-Witten transition.

Challenges are identified in defining the deformation for double scaled models.

Abstract

We define and study the $T\bar{T}$ deformation of a random matrix model, showing a consistent definition requires the inclusion of both the perturbative and non-perturbative solutions to the flow equation. The deformed model is well defined for arbitrary values of the coupling, exhibiting a phase transition for the critical value in which the spectrum complexifies. The transition is between a single and a double-cut phase, typically third order and in the same universality class as the Gross-Witten transition in lattice gauge theory. The $T\bar{T}$ deformation of a double scaled model is more subtle and complicated, and we are not able to give a compelling definition, although we discuss obstacles and possible alternatives. Preliminary comparisons with finite cut-off Jackiw-Teitelboim gravity are presented.