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The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory

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arxiv 1905.04644 v2 pith:GSMOSS5A submitted 2019-05-12 math.QA cond-mat.str-elhep-thmath.CT

Liang Kong , Yin Tian , Shan Zhou This is my paper · ORCID
classification math.QAcond-mat.str-elhep-thmath.CT
keywords centermonoidalomegacategoriescategorydijkgraaf-wittenfinitemathbf
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abstract

In this work, for a finite group $G$ and a 4-cocycle $\omega \in Z^4(G, \mathbf{k}^\times)$, we compute explicitly the center of the monoidal 2-category $\operatorname{2Vec}_G^{\omega}$ of $\omega$-twisted $G$-graded 1-categories of finite dimensional $\mathbf{k}$-vector spaces. This center gives a precise mathematical description of the topological defects in the associated 3+1D Dijkgraaf-Witten TQFT. We prove that this center is a braided monoidal 2-category with a trivial sylleptic center.

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Cited by 3 Pith papers

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