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Non-invertible Symmetries and Higher Representation Theory II
by Thomas Bartsch, Mathew Bullimore, Andrea E. V. Ferrari, Jamie Pearson
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Thomas Bartsch · Andrea Ferrari |
| Submission information | |
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| Preprint Link: | scipost_202402_00004v3 (pdf) |
| Date accepted: | 2024-08-07 |
| Date submitted: | 2024-05-29 19:47 |
| Submitted by: | Bartsch, Thomas |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
- Commented on the fact that we are only considering dressing with 3d TQFTs of Turaev-Viro type in D=4 in the last paragraph of subsection 1.1 and the third paragraph of section 4 , as incorporating more general TQFTs is beyond the scope of this paper.
Published as SciPost Phys. 17, 067 (2024)