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

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.