Non-supersymmetric duality cascade of QCD(BF) via semiclassics on $\mathbb{R}^2\times T^2$ with the baryon-'t Hooft flux

TL;DR

This paper investigates the phase structure of bifundamental QCD using semiclassical methods on a compactified space, providing evidence for a non-supersymmetric duality cascade between different gauge theories.

Contribution

It introduces a novel semiclassical approach on $ ext{R}^2 imes T^2$ with baryon-'t Hooft flux to analyze the phase diagram and explicitly constructs the duality map between parent and daughter theories.

Findings

Validated the duality cascade through semiclassical analysis.

Derived the phase diagram of QCD(BF) models.

Found strong agreement of phase diagrams between theories at finite N.

Abstract

We study the phase diagrams of the bifundamental QCD (QCD(BF)) of different ranks, which is the $4$d $SU(N_1) \times SU(N_2)$ gauge theory coupled with a bifundamental Dirac fermion. After discussing the anomaly constraints on possible vacuum structures, we apply a novel semiclassical approach on $\mathbb{R}^2\times T^2$ with the baryon-'t Hooft flux to obtain the concrete dynamics. The $2$d effective theory is derived by the dilute gas approximation of center vortices, and it serves as the basis for determining the phase diagram of the model under the assumption of adiabatic continuity. As an application, we justify the non-supersymmetric duality cascade between different QCD(BF), which has been conjectured in the large-${N}$ argument. Combined with the semiclassics and the large-$N_{1,2}$ limit, we construct the explicit duality map from the parent theory, $SU(N_1) \times SU(N_2)$ QCD(BF), to the daughter theory, $SU(N_1) \times SU(N_2-N_1)$ QCD(BF), including the correspondence of the coupling constants. We numerically examine the validity of the duality also for finite $N_{1,2}$ within our semiclassics, finding a remarkable agreement of the phase diagrams between the parent and daughter sides.