Discrete anomaly matching

Abstract

We extend the well-known 't Hooft anomaly matching conditions for continuous global symmetries to discrete groups. We state explicitly the matching conditions for all possible anomalies which involve discrete symmetries. There are two types of discrete anomalies. For Type I anomalies, the matching conditions always have to be 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 symmetric Yang-Mills theories described by the Veneziano-Yankielowicz Lagrangian and certain non-supersymmetric confining theories. The conjectured self-dual theories based in 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.