$T\overline{T}$-deformation of $q$-Yang-Mills theory

Abstract

We derive the $T\overline{T}$-perturbed version of two-dimensional $q$-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $T\overline{T}$-deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large $N$ factorization into chiral and anti-chiral sectors. For the $U(N)$ gauge theory on the sphere, we show that the large $N$ phase transition persists, and that it is of third order and induced by instantons. The effect of the $T\overline{T}$-deformation is to decrease the critical value of the 't Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for $(q,t)$-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large $N$ limit of Yang-Mills theory, showing that the $T\overline{T}$-deformation decreases the contribution of the Boltzmann entropy.

43 pages, 12 figures; v2: typos corrected, references added; v3: minor corrections; Final version published in JHEP

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Cited by in corpus (8)

• $T\bar{T}$-flow effects on torus partition functions
• $T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories
• Exact $T\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere
• Exact $T\overline{T}$ deformation of two-dimensional Maxwell theory
• $T\bar{T}$ deformation of random matrices
• $T\bar{T}$-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
• Metric approach to a $\mathrm{T}\bar{\mathrm{T}}-$like deformation in arbitrary dimensions