$T\bar{T}$ deformed YM$_{2}$ on general backgrounds from an integral transformation

Understand

We consider the $T\bar{T}$ deformation of two dimensional Yang--Mills theory on general curved backgrounds.

• We compute the deformed partition function through an integral transformation over frame fields weighted by a Gaussian kernel.
• We show that this partition function satisfies a flow equation which has been derived previously in the literature, which now holds on general backgrounds.
• We connect ambiguities associated to first derivative terms in the flow equation to the normalization of the functional integral over frame fields.