Higher form symmetries and orbifolds of two-dimensional Yang-Mills theory
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| Format: | Preprint |
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2024
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| _version_ | 1866929287015170048 |
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| author | Santilli, Leonardo Szabo, Richard J. |
| author_facet | Santilli, Leonardo Szabo, Richard J. |
| contents | 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 $θ$-angle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03119 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher form symmetries and orbifolds of two-dimensional Yang-Mills theory Santilli, Leonardo Szabo, Richard J. High Energy Physics - Theory Mathematical Physics Differential Geometry Quantum Algebra 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 $θ$-angle. |
| title | Higher form symmetries and orbifolds of two-dimensional Yang-Mills theory |
| topic | High Energy Physics - Theory Mathematical Physics Differential Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2403.03119 |