1. Higher form symmetries and orbifolds of two-dimensional Yang-Mills theory
- Author
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Santilli, Leonardo and Szabo, Richard J.
- Subjects
High Energy Physics - Theory ,Mathematical Physics ,Mathematics - Differential Geometry ,Mathematics - Quantum Algebra - 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., Comment: 55 pages, 3 figures, 1 table; v2: minor changes and additions, references added
- Published
- 2024