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arXiv · 1905.04644

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

Liang Kong·Yin Tian·Shan Zhou
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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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BibTeXRIS

Liang Kong, Yin Tian, Shan Zhou. 2019-05-12. The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory. https://doi.org/10.1016/j.aim.2019.106928

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