On Discrete Anomalies in Chiral Gauge Theories

TL;DR

This paper critically examines claims of a mod 2 anomaly in certain SU(N) chiral gauge theories, demonstrating that no such anomaly exists and providing a pathway to realize gapless fermion phases without obstruction.

Contribution

The authors refute the existence of a proposed mod 2 anomaly in specific chiral gauge theories and explicitly construct a phase with gapless fermions, clarifying the theories' phase structure.

Findings

No mod 2 anomaly exists in the studied theories.

A concrete path to realizing gapless fermion phases is provided.

Theories can confine without breaking global symmetry, contrary to previous claims.

Abstract

We study two well-known $SU(N)$ chiral gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. We give a detailed description of the global symmetry, including various discrete quotients. Recent work argues that these theories exhibit a subtle mod 2 anomaly, ruling out certain phases in which the theories confine without breaking their global symmetry, leaving a gapless composite fermion in the infra-red. We point out that no such anomaly exists. We further exhibit an explicit path to the gapless fermion phase, showing that there is no kinematic obstruction to realising these phases.