Cardy Algebras, Sewing Constraints and String-Nets
| Autor: | Traube, Matthias |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In \cite{Schweigert:2019zwt} it was shown how string-net spaces for the Cardy bulk algebra in the Drinfeld center $\mathsf{Z}(\mathsf{C})$ of a modular tensor category $\mathsf{C}$ give rise to a consistent set of correlators. We extend their results to include open-closed world sheets and allow for more general field algebras, which come in the form of $(\mathsf{C}|\mathsf{Z}(\mathsf{C}))$-Cardy algebras. To be more precise, we show that a set of fundamental string-nets with input data from a $(\mathsf{C}|\mathsf{Z}(\mathsf{C}))$-Cardy algebra gives rise to a solution of the sewing constraints formulated in \cite{Kong_2014} and that any set of fundamental string-nets solving the sewing constraints determine a $(\mathsf{C}|\mathsf{Z}(\mathsf{C}))$-Cardy algebra up to isomorphism. Hence we give an alternative proof of the results in \cite{Kong_2014} in terms of string-nets. Comment: 36 pages, lots of figures, v3: minor changes |
| Databáze: | arXiv |
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