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

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 ${2Vec}_G^{\omega }$ 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.

arXiv comment24 pages

References in corpus (4)

• Symmetry protected topological orders and the group cohomology of their symmetry group
• Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries
• Fusion 2-categories and a state-sum invariant for 4-manifolds
• The twisted Drinfeld double of a finite group via gerbes and finite groupoids

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