The symmetry enriched center functor is fully faithful
type: Item
instance of: scholarly article
title: The symmetry enriched center functor is fully faithful
zbMATH Open document ID: 1499.18033
author: Long Sun
published in: Communications in Mathematical Physics
publication date: 2022-10-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/2201.00192
review text: It was shown in [\textit{L. Kong} and \textit{H. Zheng}, Adv. Math. 339, 749--779 (2018; Zbl 1419.18013)] that the Drinfeld center can be made functorial and fully faithful provided that proper domain and codomain are chosen. This Drinfeld center provides a precise and complete mathematical description of the boundary-bulk relation of 2+1D anomaly-free topological orders with gapped boundaries [\textit{L. Kong} et al., Nucl. Phys., B 922, 62--76 (2017; Zbl 1373.82093)]. In the theory of topological orders, topological orders with symmetry is called a symmetry enriched topological (SET) order [\textit{M. Levin} and \textit{Z.-C. Gu}, ``Braiding statistics approach to symmetry protected topological phases'', Phys. Rev. B 86, No. 11, Article ID 115109, 15 p. (2012; \url{doi:10.1103/PhysRevB.86.115109}); \textit{X. Chen} et al., ``Symmetry protected topological orders and the group cohomology of their symmetry group'', Phys. Rev. B 87, No. 15, Article ID 155114, 48 p. (2013; \url{doi:10.1103/PhysRevB.87.155114}); \textit{M. Barkeshli} et al., ``Symmetry fractionalization, defects, and gauging of topological phases'', Phys. Rev. B 100, No. 11, Article ID 115147, 99 p. (2019; \url{doi:10.1103/PhysRevB.100.115147})]. This paper gives a generalization of the work in [\textit{L. Kong} and \textit{H. Zheng}, Adv. Math. 339, 749--779 (2018; Zbl 1419.18013)] to describe the symmetry enriched case, more precisely, to find categorical description of SET orders and give a notion of the symmetry enriched center and make it functorial by choosing proper domain and codomain categories. The synopsis of the paper goes as follows. \begin{itemize} \item[\S 2] gives preliminaries on finite monoidal categories. \item[\S 3] introduces a series of symmetry enriched categories, especially including finite monoidal categories over \(\mathcal{E}\) and finite braided monoidal categories containing \(\mathcal{E}\), and defines a new tensor product between the latter, named the relative tensor pro…
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 18M05
Mathematics Subject Classification ID: 18D20
Mathematics Subject Classification ID: 18M15
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 7606702
MaRDI profile type: Publication
OpenAlex ID: W4225894877
arXiv ID: 2201.00192
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DOI: 10.1007/S00220-022-04456-0
description: scientific article