$T\overline{T}$-deformation of $q$-Yang-Mills theory

TL;DR

This paper studies the effects of $T\overline{T}$-deformation on two-dimensional $q$-deformed Yang-Mills theory, revealing changes in phase transition properties, breaking of certain theoretical connections, and impacts on entanglement entropy.

Contribution

It derives the $T\overline{T}$-deformed $q$-Yang-Mills theory on arbitrary surfaces and analyzes its phase structure, connections, and entanglement entropy, extending previous models.

Findings

The $T\overline{T}$-deformation breaks the connection with Chern-Simons theory.

The large $N$ phase transition remains third order and is influenced by instantons.

Deformation lowers the critical 't Hooft coupling and broadens the phase transition conditions.

Abstract

We derive the $T\overline{T}$-perturbed version of two-dimensional $q$-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $T\overline{T}$-deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large $N$ factorization into chiral and anti-chiral sectors. For the $U(N)$ gauge theory on the sphere, we show that the large $N$ phase transition persists, and that it is of third order and induced by instantons. The effect of the $T\overline{T}$-deformation is to decrease the critical value of the 't Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for $(q,t)$-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large $N$ limit of Yang-Mills theory, showing that the $T\overline{T}$-deformation decreases the contribution of the Boltzmann entropy.