Non-invertible Symmetries and Higher Representation Theory II
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917759860867072 |
|---|---|
| author | Bartsch, Thomas Bullimore, Mathew Ferrari, Andrea E. V. Pearson, Jamie |
| author_facet | Bartsch, Thomas Bullimore, Mathew Ferrari, Andrea E. V. Pearson, Jamie |
| contents | In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the construction of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. We propose that the symmetry categories obtained by gauging higher subgroups may be defined as higher group-theoretical fusion categories, which are built from the projective higher representations of higher groups. As concrete applications we provide a unified description of the symmetry categories of gauge theories in three and four dimensions based on the Lie algebra $\mathfrak{so}(N)$, and a fully categorical description of non-invertible symmetries obtained by gauging a 1-form symmetry with a mixed 't Hooft anomaly. We also discuss the effect of discrete torsion on symmetry categories, based a series of obstructions determined by spectral sequence arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07393 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-invertible Symmetries and Higher Representation Theory II Bartsch, Thomas Bullimore, Mathew Ferrari, Andrea E. V. Pearson, Jamie High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the construction of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. We propose that the symmetry categories obtained by gauging higher subgroups may be defined as higher group-theoretical fusion categories, which are built from the projective higher representations of higher groups. As concrete applications we provide a unified description of the symmetry categories of gauge theories in three and four dimensions based on the Lie algebra $\mathfrak{so}(N)$, and a fully categorical description of non-invertible symmetries obtained by gauging a 1-form symmetry with a mixed 't Hooft anomaly. We also discuss the effect of discrete torsion on symmetry categories, based a series of obstructions determined by spectral sequence arguments. |
| title | Non-invertible Symmetries and Higher Representation Theory II |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2212.07393 |