论文标题
Cardy代数，缝纫限制和弦网
Cardy Algebras, Sewing Constraints and String-Nets
论文作者
论文摘要
在\ cite {schweigert：2019zwt}中显示了在德林菲尔德中心中的card-bulk代数的弦线空间$ \ mathsf {z}（\ mathsf {c}）$的一个模块化张量类别类别$ \ mathsf {c}的模块化张{c} $。我们将其结果扩展到包括开放式的世界表并允许更多的通用字段代数，该代数的形式为$（\ Mathsf {C} | \ Mathsf {Z}（\ Mathsf {C}））$ - Cardy代数。更准确地说，我们表明，一组基本的弦网和带有$（\ Mathsf {C} | \ Mathsf {Z} {Z}（\ Mathsf {C}）的输入数据）$ - 心脏代数会产生\ citter in \ Cite {kong_2014}的污水量的解决方案，并在\ ciite {kong_2014}中均设置了任何设置。 $（\ Mathsf {C} | \ Mathsf {Z}（\ Mathsf {C}））$ - Cardy代数为同构。因此，我们在\ cite {kong_2014}中以字符串nets表示了替代证明结果。
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.
