Higher form symmetries and orbifolds of two-dimensional Yang–Mills theory

Abstract

We undertake a detailed study of the gaugings of two-dimensional Yang–Mills theory by its intrinsic charge conjugation 0-form and centre 1-form global symmetries, elucidating their higher algebraic and geometric structures, as well as the meaning of dual lower form symmetries. Our derivations of orbifold gauge theories make use of a combination of standard continuum path integral methods, networks of topological defects, and techniques from higher gauge theory. We provide a unified description of higher and lower form gauge fields for a p-form symmetry in the geometric setting of p-gerbes, and derive reverse orbifolds by the dual \((-1)\)-form symmetries. We identify those orbifolds in which charge conjugation symmetry is spontaneously broken, and relate the breaking to mixed anomalies involving \((-1)\)-form symmetries. We extend these considerations to gaugings by the non-invertible 1-form symmetries of two-dimensional Yang–Mills theory by introducing a notion of generalized \(\theta \)-angle.