  We connect a family of gauge theories (Maxwell theories with a
magnetoelectric coupling $\theta = 2 \pi k, k \in \mathbb{Z}$) to the family of
3D topological lattice models introduced by Walker and Wang. In particular, we
show that the lattice Hamiltonians capture a certain strong-coupling limit of
these gauge theories, in which the system enters a gapped (confined) phase. We
discuss the relationship between the topological order exhibited by certain of
these lattice Hamiltonians and the characteristic electromagnetic response of
the symmetry-protected bosonic topological insulator.
