The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten theory
Copyright policy )The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten theory
In this work, for a finite group $G$ and a 4-cocycle $��\in Z^4(G, \mathbf{k}^\times)$, we compute explicitly the center of the monoidal 2-category $\operatorname{2Vec}_G^��$ of $��$-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.
24 pages
- University of California, Santa Barbara United States
- Tsinghua University China (People's Republic of)
- Southern University of Science and Technology China (People's Republic of)
High Energy Physics - Theory, Strongly Correlated Electrons (cond-mat.str-el), topological quantum field theory, FOS: Physical sciences, Mathematics - Category Theory, Topological quantum field theories (aspects of differential topology), Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Theory (hep-th), Drinfeld center, Mathematics - Quantum Algebra, FOS: Mathematics, Monoidal categories, symmetric monoidal categories, braided monoidal 2-categories, Quantum Algebra (math.QA), Category Theory (math.CT), Topological field theories in quantum mechanics, Groupoids, semigroupoids, semigroups, groups (viewed as categories)
High Energy Physics - Theory, Strongly Correlated Electrons (cond-mat.str-el), topological quantum field theory, FOS: Physical sciences, Mathematics - Category Theory, Topological quantum field theories (aspects of differential topology), Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Theory (hep-th), Drinfeld center, Mathematics - Quantum Algebra, FOS: Mathematics, Monoidal categories, symmetric monoidal categories, braided monoidal 2-categories, Quantum Algebra (math.QA), Category Theory (math.CT), Topological field theories in quantum mechanics, Groupoids, semigroupoids, semigroups, groups (viewed as categories)
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