Domain Walls in Topological Phases and the Brauer–Picard Ring for $${{\rm Vec} (\mathbb{Z}/p\mathbb{Z})}$$
| Autor: | Jacob C. Bridgeman, Daniel Barter, Corey Jones |
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| Rok vydání: | 2019 |
| Předmět: |
Physics
Ring (mathematics) Mathematics::Rings and Algebras 010102 general mathematics Statistical and Nonlinear Physics Topology 01 natural sciences Interpretation (model theory) law.invention Invertible matrix Tensor product law Mathematics::Category Theory 0103 physical sciences Domain (ring theory) Bimodule C++ string handling 010307 mathematical physics 0101 mathematics Indecomposable module Mathematical Physics |
| Zdroj: | Communications in Mathematical Physics. 369:1167-1185 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-019-03338-2 |
| Popis: | We show how to calculate the relative tensor product of bimodule categories (not necessarily invertible) using ladder string diagrams. As an illustrative example, we compute the Brauer–Picard ring for the fusion category $${{\bf Vec} (\mathbb{Z}/p\mathbb{Z})}$$ . Moreover, we provide a physical interpretation of all indecomposable bimodule categories in terms of domain walls in the associated topological phase. We show how this interpretation can be used to compute the Brauer–Picard ring from a physical perspective. |
| Databáze: | OpenAIRE |
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