• 1-form center symmetry
• chiral theories
• gauge theories
• mixed ‘t Hooft anomalies
• ‘t Hooft anomaly matching

A particular class of 4D quantum field theories, strongly-coupled chiral SU(N) gauge theories, are explored.
The introduction of the concept of generalized symmetries, has given new inputs in the study of strongly-coupled theories. Simultaneous considerations of the new type of symmetries together with conventional ones lead to novel types of anomalies, i.e., the mixed anomalies and, as in the original ’t Hooft construction, these obstruction of gauging symmetries must be appropriately reflected in the IR.
The aim of this Master Thesis is to extend these investigations and to explore a class of chiral gauge theories: tensor chiral gauge theories. These models are built by using the matter fermions in the 2-index symmetric and 2-index anti-antisymmetric tensor representations. A few models with SU(5), SU(6) and SU(8) gauge groups are studied in detail, and the mixed anomalies in these models are exhibited.
In all the models, the mixed anomaly involving the 1-form center symmetry Z_N and a certain non-anomalous U(1) symmetry is found to be present. We interpret this
anomaly as an indication of the spontaneous breaking of the U(1) symmetry, due to the formation of some bifermion condensate. The presence of such a condensate implies Higgs mechanism and flavor symmetry breaking, bringing, at low energies, the system either in a color-flavor-locked dynamical Higgs phase or into systems with IR-free Abelian or non-Abelian gauge groups. The study of a system with a certain IR-free non-Abelian gauge symmetry is new.
The idea of the Natural Anomaly Matching is discussed, which shows how, in both types of phases mentioned, the conventional as well as the new, generalized anomaly matching conditions with respect to the unbroken symmetries, are fully satisfied by the massless fermions present in the IR.