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- W3012099713 abstract "We axiomatize the extended operators in topological orders (possibly gravitationally anomalous, possibly with degenerate ground states) in terms of monoidal Karoubi-complete n-categories which are mildly dualizable and have trivial centre. Dualizability encodes the word “topological,” and we take it as the definition of “(separable) multifusion n-category”; triviality of the centre implements the physical principle of “remote detectability.” We show that such n-categorical algebras are Morita-invertible (in the appropriate higher Morita category), thereby identifying topological orders with anomalous fully-extended TQFTs. We identify centreless fusion n-categories (i.e. multifusion n-categories with indecomposable unit) with centreless braided fusion $$(n{-}1)$$ -categories. We then discuss the classification in low spacetime dimension, proving in particular that all $$(1{+}1)$$ - and $$(3{+}1)$$ -dimensional topological orders, with arbitrary symmetry enhancement, are suitably-generalized topological sigma models. These mathematical results confirm and extend a series of conjectures and results by L. Kong, X.G. Wen, and their collaborators." @default.
- W3012099713 created "2020-03-23" @default.
- W3012099713 creator A5074192674 @default.
- W3012099713 date "2022-04-16" @default.
- W3012099713 modified "2023-10-12" @default.
- W3012099713 title "On the Classification of Topological Orders" @default.
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- W3012099713 doi "https://doi.org/10.1007/s00220-022-04380-3" @default.
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