The phase diagram of $$ T\overline{T} $$-deformed Yang-Mills theory on the sphere

Abstract

We study the large-N dynamics of $$ T\overline{T} $$ T T ¯ -deformed two-dimensional Yang-Mills theory at genus zero. The 1/N-expansion of the free energy is obtained by exploiting the associated flow equation and the complete phase diagram of the theory is derived for both signs of the rescaled deformation parameter τ. We observe a third-order phase transition driven by instanton condensation, which is the deformed version of the familiar Douglas-Kazakov transition separating the weakly-coupled from the strongly-coupled phase. By studying these phases, we compute the deformation of both the perturbative sector and the Gross-Taylor string expansion. Nonperturbative corrections in τ drive the system into an unexplored disordered phase separated by a novel critical line meeting tangentially the Douglas-Kazakov one at a tricritical point. The associated phase transition is induced by the collision of large-N saddle points, determining its second-order character.

Exact $$ T\overline{T} $$ deformation of two-dimensional Yang-Mills theory on the sphere

“…1 Furthermore, it is natural to employ our analysis of the flow equation to extend previous results at large N [20,21]. In [26], we obtain the full 1/N expansion of the deformed theory by studying the differential equation governing the deformation of the free energy in the large-N limit. This, in turn, allows us to study the full phase diagram of the deformed theory.…”