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.
Categories: hep-th