Non-invertible symmetries and higher representation theory I

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

Abstract

The purpose of this paper is to investigate the global categorical symmetries that arise when gauging finite higher groups in three or more dimensions. The motivation is to provide a common perspective on constructions of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. This paper focusses on gauging finite groups and split 2-groups in three dimensions. In addition to topological Wilson lines, we show that this generates a rich spectrum of topological surface defects labelled by 2-representations and explain their connection to condensation defects for Wilson lines. We derive various properties of the topological defects and show that the associated symmetry category is the fusion 2-category of 2-representations. This allows us to determine the full symmetry categories of certain gauge theories with disconnected gauge groups. A subsequent paper will examine gauging more general higher groups in higher dimensions.

Citation

Bartsch, T., Bullimore, M., Ferrari, A. E. V., & Pearson, J. (2024). Non-invertible symmetries and higher representation theory I. SciPost Physics, 17(1), Article 015. https://doi.org/10.21468/scipostphys.17.1.015

• Journal Article Type: Article
• Acceptance Date: May 27, 2024
• Online Publication Date: Jul 16, 2024
• Publication Date: Jul 15, 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: 1
• Article Number: 015
• DOI: https://doi.org/10.21468/scipostphys.17.1.015
• Public URL: https://durham-repository.worktribe.com/output/2874421