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

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