2-Group symmetries and their classification in 6d

Apruzzi, Fabio; Bhardwaj, Lakshya; Gould, Dewi S. W.; Schäfer-Nameki, Sakura

doi:10.21468/SciPostPhys.12.3.098

SciPost Physics

2-Group symmetries and their classification in 6d

Fabio Apruzzi, Lakshya Bhardwaj, Dewi S. W. Gould, Sakura Schäfer-Nameki

SciPost Phys. 12, 098 (2022) · published 18 March 2022

doi: 10.21468/SciPostPhys.12.3.098
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Abstract

We uncover 2-group symmetries in 6d superconformal field theories. These symmetries arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory mix with each other. We classify all 6d superconformal field theories with such 2-group symmetries. The approach taken in 6d is applicable more generally, with minor modifications to include dimension specific operators (such as instantons in 5d and monopoles in 3d), and we provide a discussion of the dimension-independent aspects of the analysis. We include an ancillary mathematica code for computing 2-group symmetries, once the dimension specific input is provided. We also discuss a mixed 't Hooft anomaly between discrete 0-form and 1-form symmetries in 6d.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.3.098
TI  - 2-Group symmetries and their classification in 6d
PY  - 2022/03/18
UR  - https://scipost.org/SciPostPhys.12.3.098
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 3
SP  - 098
A1  - Apruzzi, Fabio
AU  - Bhardwaj, Lakshya
AU  - Gould, Dewi S. W.
AU  - Schäfer-Nameki, Sakura
AB  - We uncover 2-group symmetries in 6d superconformal field theories. These symmetries arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory mix with each other. We classify all 6d superconformal field theories with such 2-group symmetries. The approach taken in 6d is applicable more generally, with minor modifications to include dimension specific operators (such as instantons in 5d and monopoles in 3d), and we provide a discussion of the dimension-independent aspects of the analysis. We include an ancillary mathematica code for computing 2-group symmetries, once the dimension specific input is provided. We also discuss a mixed 't Hooft anomaly between discrete 0-form and 1-form symmetries in 6d.
ER  -

@Article{10.21468/SciPostPhys.12.3.098,
	title={{2-Group symmetries and their classification in 6d}},
	author={Fabio Apruzzi and Lakshya Bhardwaj and Dewi S. W. Gould and Sakura Schäfer-Nameki},
	journal={SciPost Phys.},
	volume={12},
	pages={098},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.3.098},
	url={https://scipost.org/10.21468/SciPostPhys.12.3.098},
}

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Funders for the research work leading to this publication

European Research Council [ERC]
Horizon 2020 (through Organization: European Commission [EC])
Simons Foundation