Semiclassical analysis of the bifundamental QCD on ℝ2 × T2 with ’t Hooft flux

Abstract

Abstract We study the phase structure of bifundamental quantum chromodynamics (QCD(BF)), which is the 4-dimensional SU(N) × SU(N) gauge theory coupled with the bifundamental fermion. Firstly, we refine constraints on its phase diagram from ’t Hooft anomalies and global inconsistencies, and we find more severe constraints than those in previous literature about QCD(BF). Secondly, we employ the recently-proposed semiclassical approach for confining vacua to investigate this model concretely, and this is made possible via anomaly-preserving T2 compactification. For sufficiently small T2 with the ’t Hooft flux, the dilute gas approximation of center vortices gives reliable semiclassical computations, and we determine the phase diagram as a function of the fermion mass m, two strong scales Λ1, Λ2, and two vacuum angles, θ1, θ2. In particular, we find that the QCD(BF) vacuum respects the ℤ2 exchange symmetry of two gauge groups. Under the assumption of the adiabatic continuity, our result successfully explains one of the conjectured phase diagrams in the previous literature and also gives positive support for the nonperturbative validity of the large-N orbifold equivalence between QCD(BF) and $$ \mathcal{N} $$ N = 1 SU(2N) supersymmetric Yang-Mills theory. We also comment on problems of domain walls.