Exact $T\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere

TL;DR

This paper analyzes the exact $Tar{T}$ deformation of 2D Yang-Mills theory on a sphere, revealing how nonperturbative effects and flux sectors influence the deformed partition function.

Contribution

It provides a detailed instanton-level analysis of the $Tar{T}$ deformation in 2D Yang-Mills, including nonperturbative contributions and flux sector solutions.

Findings

For $mbda>0$, the partition function sums over a finite set of representations.

For $mbda<0$, nonperturbative effects regularize the partition function.

The deformation modifies the spectrum and introduces nontrivial subtractions for negative deformation parameters.

Abstract

We study the $T\bar{T}$ deformation of two-dimensional Yang-Mills theory at genus zero by carrying out the analysis at the level of its instanton representation. We first focus on the perturbative sector by considering its power expansion in the deformation parameter $\mu$. By studying the resulting asymptotic series through resurgence theory, we determine the nonperturbative contributions that enter the result for $\mu<0$. We then extend this analysis to any flux sector by solving the relevant flow equation. Specifically, we impose boundary conditions corresponding to two distinct regimes: the quantum undeformed theory and the semiclassical limit of the deformed theory. The full partition function is obtained as a sum over all magnetic fluxes. For any $\mu>0$, only a finite portion of the quantum spectrum survives and the partition function reduces to a sum over a finite set of representations. For $\mu<0$, nonperturbative contributions regularize the partition function through an intriguing mechanism that generates nontrivial subtractions.