Non-invertible higher-categorical symmetries
Lakshya Bhardwaj, Lea E. Bottini, Sakura Schäfer-Nameki, Apoorv Tiwari
SciPost Phys. 14, 007 (2023) · published 26 January 2023
- doi: 10.21468/SciPostPhys.14.1.007
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Abstract
We sketch a procedure to capture general non-invertible symmetries of a $d$-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also discuss fusions of topological defects, which involve condensations/gaugings of higher-categorical symmetries localized on the worldvolumes of topological defects. Recently some fusions of topological defects were discussed in the literature where the dimension of topological defects seems to jump under fusion. This is not possible in the standard description of higher-categories. We explain that the dimension-changing fusions are understood as higher-morphisms of the higher-category describing the symmetry. We also discuss how a 0-form sub-symmetry of a higher-categorical symmetry can be gauged and describe the higher-categorical symmetry of the theory obtained after gauging. This provides a procedure for constructing non-invertible higher-categorical symmetries starting from invertible higher-form or higher-group symmetries and gauging a 0-form symmetry. We illustrate this procedure by constructing non-invertible 2-categorical symmetries in 4d gauge theories and non-invertible 3-categorical symmetries in 5d and 6d theories. We check some of the results obtained using our approach against the results obtained using a recently proposed approach based on 't Hooft anomalies.
TY - JOUR
PB - SciPost Foundation
DO - 10.21468/SciPostPhys.14.1.007
TI - Non-invertible higher-categorical symmetries
PY - 2023/01/26
UR - https://scipost.org/SciPostPhys.14.1.007
JF - SciPost Physics
JA - SciPost Phys.
VL - 14
IS - 1
SP - 007
A1 - Bhardwaj, Lakshya
AU - Bottini, Lea E.
AU - Schäfer-Nameki, Sakura
AU - Tiwari, Apoorv
AB - We sketch a procedure to capture general non-invertible symmetries of a $d$-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also discuss fusions of topological defects, which involve condensations/gaugings of higher-categorical symmetries localized on the worldvolumes of topological defects. Recently some fusions of topological defects were discussed in the literature where the dimension of topological defects seems to jump under fusion. This is not possible in the standard description of higher-categories. We explain that the dimension-changing fusions are understood as higher-morphisms of the higher-category describing the symmetry. We also discuss how a 0-form sub-symmetry of a higher-categorical symmetry can be gauged and describe the higher-categorical symmetry of the theory obtained after gauging. This provides a procedure for constructing non-invertible higher-categorical symmetries starting from invertible higher-form or higher-group symmetries and gauging a 0-form symmetry. We illustrate this procedure by constructing non-invertible 2-categorical symmetries in 4d gauge theories and non-invertible 3-categorical symmetries in 5d and 6d theories. We check some of the results obtained using our approach against the results obtained using a recently proposed approach based on 't Hooft anomalies.
ER -@Article{10.21468/SciPostPhys.14.1.007,
title={{Non-invertible higher-categorical symmetries}},
author={Lakshya Bhardwaj and Lea E. Bottini and Sakura Schäfer-Nameki and Apoorv Tiwari},
journal={SciPost Phys.},
volume={14},
pages={007},
year={2023},
publisher={SciPost},
doi={10.21468/SciPostPhys.14.1.007},
url={https://scipost.org/10.21468/SciPostPhys.14.1.007},
}
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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
- Vetenskapsrådet / Swedish Research Council