Disentangling modular Walker-Wang models via fermionic invertible boundaries

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 unitary modular tensor category. We also discuss general (noninvertible) boundaries of general Walker-Wang models and describe a simple axiomatization of extended topological quantum field theory in terms of tensors.