Non-invertible Symmetries and Higher Representation Theory I

Understand

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.