Dynamical Abelianization and anomalies in chiral gauge theories

TL;DR

This paper investigates the infrared behavior of a specific strongly-coupled chiral $SU(N)$ gauge theory, proposing that dynamical Abelianization and anomaly considerations can elucidate its low-energy dynamics.

Contribution

It introduces a detailed analysis of the infrared dynamics of a chiral $SU(N)$ gauge theory using dynamical Abelianization and anomaly matching, extending understanding of strongly-coupled chiral theories.

Findings

Infrared dynamics consistent with dynamical Abelianization.

Mixed anomaly analysis supports the proposed low-energy behavior.

Symmetry realization aligns with the anomaly constraints.

Abstract

We explore the idea that in some class of strongly-coupled chiral $SU(N)$ gauge theories the infrared dynamics might be characterized by a bifermion condensate in the adjoint representation of the color gauge group. As an illustration, in this work we revisit an $SU(N)$ chiral gauge theory with Weyl fermions in a symmetric ($\psi$) and anti-antisymmetric ($\chi$) tensor representations, together with eight fermions in the anti-fundamental representations ($\eta$), which we called $\psi\chi\eta$ model in the previous investigations. We study the infrared dynamics of this system more carefully, by assuming dynamical Abelianization, a phenomenon familiar from ${\cal N}=2$ supersymmetric gauge theories, and by analyzing the way various continuous and discrete symmetries are realized at low energies. We submit then these ideas to a more stringent test, by taking into account some higher-form symmetries and the consequent mixed anomalies. A detailed analysis of the mixed anomalies involving certain $0$-form $U(1)$ symmetries and the color-flavor locked $1$-form $Z_N$ symmetry in the $\psi\chi\eta$ system shows that the proposed infrared dynamics is consistent with it.