Discrete Anomaly Matching

TL;DR

This paper extends 't Hooft anomaly matching conditions to discrete symmetries, providing criteria for anomaly consistency in supersymmetric and non-supersymmetric gauge theories, and tests these conditions on various models.

Contribution

It formulates discrete anomaly matching conditions for all anomalies involving discrete symmetries and applies them to analyze supersymmetric and other gauge theories.

Findings

Most supersymmetric solutions satisfy discrete anomaly matching.

Excluded models include certain pure supersymmetric Yang-Mills theories.

Self-dual theories with exceptional gauge groups often violate anomaly matching.

Abstract

We extend the well-known 't Hooft anomaly matching conditions for continuous global symmetries to discrete groups. We state the matching conditions for all possible anomalies which involve discrete symmetries explicitly. There are two types of discrete anomalies. For Type I anomalies, the matching conditions have to be always satisfied regardless of the details of the massive bound state spectrum. The Type II anomalies have to be also matched except if there are fractionally charged massive bound states in the theory. We check discrete anomaly matching in recent solutions of certain N=1 supersymmetric gauge theories, most of which satisfy these constraints. The excluded examples include the chirally symmetric phase of N=1 pure supersymmetric Yang-Mills theories described by the Veneziano-Yankielowicz Lagrangian and certain non-supersymmetric confining theories. The conjectured self-dual theories based on exceptional gauge groups do not satisfy discrete anomaly matching nor mapping of operators, and are viable only if the discrete symmetry in the electric theory appears as an accidental symmetry in the magnetic theory and vice versa.