${T\overline{T}}$-like Flows of Yang-Mills Theories

TL;DR

This paper explores ${Tar{T}}$-like deformations of higher-dimensional Yang-Mills theories, providing exact solutions for metric flows and stress-energy tensors, and introduces new single-trace deformations related to the non-Abelian Born-Infeld action.

Contribution

It offers the first closed-form solutions for ${Tar{T}}$-like deformations in non-Abelian Yang-Mills theories and introduces novel single-trace deformations.

Findings

Exact metric flow solutions obtained

Instanton solutions remain undeformed

Connection to non-Abelian Born-Infeld Lagrangian

Abstract

We study ${T\overline{T}}$-like deformations of $d>2$ Yang-Mills theories. The standard ${T\overline{T}}$ flows lead to multi-trace Lagrangians, and the non-Abelian gauge structures make it challenging to find Lagrangians in a closed form. However, within the geometric approach to ${T\overline{T}}$, we obtain the closed-form solution to the metric flow and stress-energy tensor, and show that instanton solutions are undeformed. We also introduce new symmetrised single-trace ${T\overline{T}}$-like deformations, whose solutions in $d=4$ include the non-Abelian Born-Infeld Lagrangian proposed by Tseytlin in 1997.