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

Abstract

Abstract We study the T T ¯ $$ T\overline{T} $$ 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 μ. By studying the resulting asymptotic series through resurgence theory, we determine the nonperturbative contributions that enter the result for μ 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 μ < 0, nonperturbative contributions regularize the partition function through an intriguing mechanism that generates nontrivial subtractions.

Keywords

• Field Theories in Lower Dimensions
• Gauge Symmetry
• Nonperturbative Ef- fects
• Topological Field Theories