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.

55 pages, 3 figures, 1 table; v2: minor changes and additions, references added