Non-invertible higher-categorical symmetries
By Lakshya Bhardwaj, Lea E. Bottini, Sakura Schafer-Nameki, A. Tiwari. SciPost Physics, 2022
146 citations recorded by the source corpus.
We sketch a procedure to capture general non-invertible symmetries of a dd-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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2a259e0fe49613d8430fb4794ed83b70c942c2a3
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Universal Non‐Invertible Symmetries (2022, methodology): “10) Indeed it was found in [3] that the categorical symmetry of pure 3d Pin(4N) gauge theory is described by Rep(D8).”