TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.4.093
TI  - Generalized charges, part I: Invertible symmetries and higher representations
PY  - 2024/04/04
UR  - https://www.scipost.org/SciPostPhys.16.4.093
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 4
SP  - 093
A1  - Bhardwaj, Lakshya
AU  - Schäfer-Nameki, Sakura
AB  - $q$-charges describe the possible actions of a generalized symmetry on $q$-dimensional operators. In Part I of this series of papers, we describe $q$-charges for invertible symmetries; while the discussion of $q$-charges for non-invertible symmetries is the topic of Part II. We argue that $q$-charges of a standard global symmetry, also known as a 0-form symmetry, correspond to the so-called $(q+1)$-representations of the 0-form symmetry group, which are natural higher-categorical generalizations of the standard notion of representations of a group. This generalizes already our understanding of possible charges under a 0-form symmetry! Just like local operators form representations of the 0-form symmetry group, higher-dimensional extended operators form higher-representations. This statement has a straightforward generalization to other invertible symmetries: $q$-charges of higher-form and higher-group symmetries are $(q+1)$-representations of the corresponding higher-groups. There is a natural extension to higher-charges of non-genuine operators (i.e. operators that are attached to higher-dimensional operators), which will be shown to be intertwiners of higher-representations. This brings into play the higher-categorical structure of higher-representations. We also discuss higher-charges of twisted sector operators (i.e. operators that appear at the boundary of topological operators of one dimension higher), including operators that appear at the boundary of condensation defects.
ER  -

@Article{10.21468/SciPostPhys.16.4.093,
	title={{Generalized charges, part I: Invertible symmetries and higher representations}},
	author={Lakshya Bhardwaj and Sakura Schäfer-Nameki},
	journal={SciPost Phys.},
	volume={16},
	pages={093},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.4.093},
	url={https://scipost.org/10.21468/SciPostPhys.16.4.093},
}