TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.1.015
TI  - Non-invertible symmetries and higher representation theory I
PY  - 2024/07/16
UR  - https://scipost.org/SciPostPhys.17.1.015
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 1
SP  - 015
A1  - Bartsch, Thomas
AU  - Bullimore, Mathew
AU  - Ferrari, Andrea E. V.
AU  - Pearson, Jamie
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.17.1.015,
	title={{Non-invertible symmetries and higher representation theory I}},
	author={Thomas Bartsch and Mathew Bullimore and Andrea E. V. Ferrari and Jamie Pearson},
	journal={SciPost Phys.},
	volume={17},
	pages={015},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.1.015},
	url={https://scipost.org/10.21468/SciPostPhys.17.1.015},
}