Discrete Anomaly Matching

TL;DR

<3-5 sentence high-level summary> The paper extends 't Hooft anomaly matching to discrete global symmetries by formulating Type I and Type II discrete anomalies and showing how they must match between UV and IR. It provides two complementary arguments (instanton-based and spurion-based) to derive the matching conditions and applies them to a broad set of N=1 SUSY gauge theories, including Seiberg duals and various s-confining examples, to test consistency. The results demonstrate that discrete anomaly matching is a powerful non-perturbative constraint that often exactly mirrors the operator mappings in dual descriptions, while excluding several proposed nonperturbative phases (e.g., certain chirally symmetric vacua and some self-dual exceptional-group theories). Overall, the work strengthens the role of discrete symmetries as essential probes of infrared dynamics in gauge theories and guides the viability of proposed low-energy spectra.

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.