$T\bar{T}$ deformed YM${}_2$ on general backgrounds from an integral transformation

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.

17 pages, no figures, references updated, minor corrections and expanded discussions in v3

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• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Exact $T\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Exact $T\overline{T}$ deformation of two-dimensional Maxwell theory
• $T\bar{T}$-deformed 2D Yang-Mills at large N: collective field theory and phase transitions
• The phase diagram of $T\bar{T}$-deformed Yang-Mills theory on the sphere