Gauging 1-form center symmetries in simple $SU(N)$ gauge theories

TL;DR

This paper explores the effects of gauging 1-form center symmetries in various simple $SU(N)$ gauge theories, revealing how mixed anomalies constrain the infrared dynamics and phase structure of these models.

Contribution

It systematically analyzes the consequences of gauging $Z_k^C$ center symmetries in multiple $SU(N)$ gauge theories, providing new insights into their infrared phases.

Findings

Mixed 't Hooft anomalies constrain IR phases.

Certain gauge theories have limited possible IR behaviors.

Gauging center symmetries helps identify phase structures.

Abstract

Consequences of gauging exact $Z_k^C$ center symmetries in several simple $SU(N)$ gauge theories, where $k$ is a divisor of $N$, are investigated. Models discussed include: the $SU(N)$ gauge theory with $N_f$ copies of Weyl fermions in self-adjoint single-column antisymmetric representation, the well-discussed adjoint QCD, QCD-like theories in which the quarks are in a two-index representation of $SU(N)$, and a chiral $SU(N)$ theory with fermions in the symmetric as well as in anti-antisymmetric representations but without fundamentals. Mixed 't Hooft anomalies between the 1-form $Z_k^C$ symmetry and some 0-form (standard) discrete symmetry provide us with useful information about the infrared dynamics of the system. In some cases they give decisive indication to select only few possiblities for the infrared phase of the theory.