Strong anomaly and phases of chiral gauge theories (2105.03921v3)

Abstract: We present a simple argument which seems to favor, when applied to a large class of strongly-coupled chiral gauge theories, a dynamical-Higgs-phase scenario, characterized by certain bifermion condensates. Flavor symmetric confining vacua described in the infrared by a set of baryonlike massless composite fermions saturating the conventional 't Hooft anomaly matching equations, appear instead disfavored. Our basic criterion is that it should be possible to write a strong-anomaly effective action, analogous to the one used in QCD to describe the solution of the $U(1)_A$ problem in the low-energy effective action, by using the low-energy degrees of freedom in the hypothesized infrared theory. We also comment on some well-known ideas such as the complementarity and the large $N$ planar dominance in the context of these chiral gauge theories.Some striking analogies and contrasts between the massless QCD and chiral gauge theories seem to emerge from this discussion.