TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.2.067
TI  - Non-invertible symmetries and higher representation theory II
PY  - 2024/08/26
UR  - https://scipost.org/SciPostPhys.17.2.067
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 2
SP  - 067
A1  - Bartsch, Thomas
AU  - Bullimore, Mathew
AU  - Ferrari, Andrea E. V.
AU  - Pearson, Jamie
AB  - 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 $\mathfrak{so}(N)$, 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.
ER  -

@Article{10.21468/SciPostPhys.17.2.067,
	title={{Non-invertible symmetries and higher representation theory II}},
	author={Thomas Bartsch and Mathew Bullimore and Andrea E. V. Ferrari and Jamie Pearson},
	journal={SciPost Phys.},
	volume={17},
	pages={067},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.2.067},
	url={https://scipost.org/10.21468/SciPostPhys.17.2.067},
}