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

TL;DR

This paper analyzes the $Tar{T}$ deformation of 2D Yang--Mills theory on curved backgrounds, deriving the deformed partition function via an integral transformation and exploring its implications for entanglement entropy and string theory connections.

Contribution

It extends the understanding of $Tar{T}$ deformations to general curved backgrounds and provides a novel integral transformation method for the deformed partition function.

Findings

Partition function satisfies a known flow equation on curved backgrounds.

Connection established between flow equation ambiguities and frame field integral normalization.

Computed entanglement entropy for general states in the deformed theory.

Abstract

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. We then compute the entanglement entropy for a general state in the theory. The connection to the string theoretic description of the theory is also investigated.