Chiral gauge theories, generalized anomalies and breakdown of the color-flavor-locked center symmetry

TL;DR

This paper investigates the nonperturbative dynamics of certain 4D chiral SU(N) gauge theories, revealing how anomalies and condensate formation lead to symmetry breaking and the loss of center symmetry, advancing understanding of their phase structure.

Contribution

It extends previous analyses of chiral gauge theories by incorporating generalized anomalies and demonstrates how anomaly matching constrains the possible infrared phases.

Findings

Dynamical Higgs phases are favored by anomaly matching.

Color-flavor-locked center symmetry is broken in the infrared.

The study provides solutions satisfying both conventional and generalized anomaly conditions.

Abstract

We study the strong-interaction dynamics of a class of $4D$ chiral $SU(N)$ gauge theories with a fermion in a symmetric second-rank tensor representation and a number of fermions in an anti-antisymmetric tensor representation, extending the previous work on chiral gauge theories such as the Bars-Yankielowicz and the generalized Georgi-Glashow models. The main tool of our analysis is the anomalies obstructing the gauging of certain 1-form color-flavor-locked center symmetry, together with some flavor symmetries. The matching requirement for these mixed-anomalies strongly favors dynamical Higgs phases caused by bifermion condensate formation, against a confinement phase with no condensates and no symmetry breaking, or a confinement phase with multifermion color-singlet condensates only. Dynamical gauge symmetry breaking and the spontaneous breaking of a $U(1)$ symmetry caused by such condensates mean that the color-flavor-locked 1-form center symmetry itself is lost in the infrared. One is led to a solution, if not unique, which satisfies fully the conventional as well as the new, generalized 't Hooft anomaly matching requirements.