Disentangling modular Walker-Wang models via fermionic invertible boundaries

• URL: http://arxiv.org/abs/2208.03397v2
• Date: Tue, 4 Oct 2022 15:03:41 GMT
• Title: Disentangling modular Walker-Wang models via fermionic invertible boundaries
• Authors: Andreas Bauer
• Abstract summary: Walker-Wang models are fixed-point models of topological order in $3+1$ dimensions constructed from a braided fusion category. We explicitly show triviality of the model by constructing an invertible domain wall to vacuum and a disentangling local unitary circuit. We also discuss general (non-invertible) boundaries of general Walker-Wang models and describe a simple axiomatization of extended TQFT in terms of tensors.
• Score: 1.479413555822768
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 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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