论文标题
通过Fermionic可逆边界解开模块化Walker-Wang模型
Disentangling modular Walker-Wang models via fermionic invertible boundaries
论文作者
论文摘要
Walker-Wang型号是从编织融合类别构建的$ 3+1 $尺寸的拓扑顺序的定点模型。对于模块化输入类别$ \ MATHCAL M $，该模型本身是可逆的，并且据信处于微不足道的拓扑阶段，而其标准边界则代表了$ 2+1 $维度的手性阶段。在这项工作中，我们通过构建可逆域壁上的真空壁，以及在$ \ Mathcal M $是Drinfeld中心的情况下，明确显示了模型的微不足道。此外，我们表明，如果我们允许在解开域壁或电路内部使用费米（辅助）自由度，那么对于较大的模块化融合类别，模型就会变得微不足道，即由Ising UMTC产生的WITT类中的模型。在附录中，我们还讨论了一般Walker-Wang模型的一般（不可逆转）边界，并用张量来描述扩展TQFT的简单公理化。
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.
