Non-invertible symmetries and higher representation theory I
Thomas Bartsch, Mathew Bullimore, Andrea E. V. Ferrari, Jamie Pearson
SciPost Phys. 17, 015 (2024) · published 16 July 2024
- doi: 10.21468/SciPostPhys.17.1.015
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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.
Cited by 19
Authors / Affiliation: mappings to Contributors and Organizations
See all Organizations.- 1 Thomas Bartsch,
- 1 Mathew Bullimore,
- 1 Andrea E. V. Ferrari,
- 1 Jamie Pearson