Title: Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality

Abstract: We introduce a class of gauge theories whose gauge group is semi-direct product of a continuous abelian and discrete non-abelian gauge groups. We call this class as semi-abelian theories. These theories may also be viewed as coupling of topological QFT to a gauge theory. This class differ from other knowns calculable theories (such as Polyakov, Seiberg-Witten, QCD(adj)) as the non-abelian part is unhiggsed, and as such, its properties are closer to pure Yang-Mills theory. In a 3d example I will describe, mass gap and string tensions are calculable. String tensions do not obey N-ality rule. We describe this phenomenon by a new exotic non-invertible symmetry, which do not form a group structure but genuine 1-form symmetry of the theory. We expect that non-invertible symmetry plays a prominent role both in Yang-Mills theory and QCD with fundamental fermions, and may provide a precise criterion for confinement in theories without exact center symmetry.

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