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

Abstract

We derive the T 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 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 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 Tdeformation decreases the contribution of the Boltzmann entropy.

Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs

“…These deformed theories can be well controlled by the fact that many quantities in the deformed theory, such as S-matrix, energy spectrum, wilson loop, correlation functions, entanglement entropy and so on can be computed analytically [2,8,33,34,35,36,37,38,39], in particular when the un-deformed theory is a CFT. These deformations also attracts much further attention from both field theory [40,41,42,43,44,45,46,47,48,49,50,51] and holographic perspectives [52,53,54,55,56,57,58,59,60,61,62,63].…”

$T\bar T$ deformation of Calogero-Sutherland model via dimensional reduction

“…It is based on the factorization of the gauge theory into chiral and anti-chiral sectors in the large N limit, which follows immediately from the fermionic picture. The T T -YM/string theory correspondence has been recently discussed [32,33]. It has been shown that the T T -YM theory is mapped onto a system of fermions experiencing highly non-local interaction that prevents their factorization.…”

“…The T T deformation of the YM theory has been studied in various contexts [29][30][31][32] by now. Also, new phenomena have been discovered [33,34]. The clear particle-like interpretation, though, seems to have been lost after the deformation.…”

$T\bar{T}$-deformed 2D Yang-Mills at large N: collective field theory and phase transitions

“…In this section we present a few comments on the recent paper [31]. We analyze the peculiarities of the DK phase transition in T T -deformed q-YM on a sphere for p ≤ 2.…”

“…The deformation preserves the order of the transition and its instanton interpretation but the critical area gets renormalized non-trivially A → Ab ∞ (τ, A). The DK phase transition for the T 2 deformed 2d q-YM theory has been discussed as well [31]. It was emphasized that the free fermion picture for the T 2 deformed theory is lost.…”