Probing the dynamics of chiral SU(N) gauge theories via generalized anomalies

TL;DR

This paper investigates chiral SU(N) gauge theories using generalized anomalies, revealing that certain models cannot maintain full chiral symmetry upon confinement, implying dynamical symmetry breaking.

Contribution

It extends previous anomaly analyses to a broader class of chiral SU(N) models, demonstrating constraints on their infrared symmetry realization.

Findings

Generalized anomalies forbid full chiral symmetry in many models.

Confinement likely involves dynamical symmetry breaking via bifermion condensates.

Results challenge traditional anomaly matching expectations.

Abstract

We study symmetries and dynamics of chiral $SU(N)$ gauge theories with matter Weyl fermions in a two-index symmetric ($\psi$) or anti-symmetric tensor ($\chi$) representation, together with $N \pm 4 + p $ fermions in the anti-fundamental ($\eta$) and $p$ fermions in the fundamental ($\xi$) representations. They are known as the Bars-Yankielowicz (the former) and the generalized Georgi-Glashow models (the latter). The conventional 't Hooft anomaly matching algorithm is known to allow a confining, chirally symmetric vacuum in all these models, with a simple set of massless baryonlike composite fermions describing the infrared physics. We analyzed recently one of these models ($\psi\eta$ model), by applying the ideas of generalized symmetries and the consequent, stronger constraints involving certain mixed anomalies, finding that the confining, chirally symmetric, vacuum is actually inconsistent. In the present paper this result is extended to a wider class of the Bars-Yankielowicz and the generalized Georgi-Glashow models. It is shown that for all these models with $N$ and $p$ both even, at least, the generalized anomaly matching requirement forbids the persistence of the full chiral symmetries in the infrared if the system confines. The most natural and consistent possibility is that some bifermion condensates form, breaking the color gauge symmetry dynamically, together with part of the global symmetry.