通过费米子可逆边界解开模块化Walker-Wang模型
Disentangling modular Walker-Wang models via fermionic invertible boundaries
摘要：
Walker-Wang模型是一种在$3+1$维上拓扑有序的固定点模型，它是由一个编织融合范畴构造的。对于一个模输入范畴$\mathcal M$，模型本身是可逆的，并且被认为是在一个平凡的拓扑相，而它的标准边界应该代表一个$2+1$维手征相。在这项工作中，我们明确地显示平凡的模型，通过构建一个可逆的畴壁真空以及解开广义局域酉电路的情况下，$\mathcal M$是一个Drinfeld中心。此外，我们表明，如果我们允许费米（辅助）自由度内的解纠缠域壁或电路，模型变得平凡的一个更大的类的模块化融合类别，即那些在维特类产生的伊辛UMTC。在附录中，我们还讨论了一般的（不可逆的）一般沃克-王模型的边界，并描述了一个简单的公理化的扩展TQFT张量。
英文摘要：
Walker-Wang models are fixed-point models of topological order in $3+1$ dimensions constructed from a braided fusion category. For a modular input category $\mathcal M$, the model itself is invertible and is believed to be in a trivial topological phase, whereas its standard boundary is supposed to represent a $2+1$-dimensional chiral phase. In this work we explicitly show triviality of the model by constructing an invertible domain wall to vacuum as well as a disentangling generalized local unitary circuit in the case where $\mathcal M$ is a Drinfeld center. Moreover, we show that if we allow for fermionic (auxiliary) degrees of freedom inside the disentangling domain wall or circuit, the model becomes trivial for a larger class of modular fusion categories, namely those in the Witt classes generated by the Ising UMTC. In the appendices, we also discuss general (non-invertible) boundaries of general Walker-Wang models and describe a simple axiomatization of extended TQFT in terms of tensors.
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