Non-invertible symmetries and higher representation theory II

Bartsch, Thomas; Bullimore, Mathew; Ferrari, Andrea E. V.; Pearson, Jamie

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 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.

Citation

Bartsch, T., Bullimore, M., Ferrari, A. E. V., & Pearson, J. (2024). Non-invertible symmetries and higher representation theory II. SciPost Physics, 17(2), Article 067. https://doi.org/10.21468/scipostphys.17.2.067

• Journal Article Type: Article
• Acceptance Date: Aug 7, 2024
• Online Publication Date: Aug 26, 2024
• Publication Date: Aug 26, 2024
• Deposit Date: Sep 23, 2024
• Publicly Available Date: Sep 23, 2024
• Journal: SciPost Physics
• Print ISSN: 2542-4653
• Electronic ISSN: 2542-4653
• Publisher: SciPost
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 2
• Article Number: 067
• DOI: https://doi.org/10.21468/scipostphys.17.2.067
• Public URL: https://durham-repository.worktribe.com/output/2874466