Large $N$ phase transition in $T \overline{T}$-deformed $2d$ Yang-Mills theory on the sphere

TL;DR

This paper investigates how a specific deformation affects the phase transition in 2D Yang-Mills theory on a sphere, revealing that the transition persists but occurs at a lower critical area, with instanton effects also playing a role.

Contribution

It demonstrates that the Douglas-Kazakov phase transition remains under $T ar{T}$ deformation and characterizes the instanton contributions in this deformed setting.

Findings

The phase transition persists under deformation.

The critical area for the transition is reduced.

Instanton contributions are explicitly characterized.

Abstract

We study the partition function of a $T \overline{T}$-deformed version of Yang-Mills theory on the two-sphere. We show that the Douglas-Kazakov phase transition persists for a range of values of the deformation parameter, and that the critical area is lowered. The transition is of third order and also induced by instantons, whose contributions we characterize.