  We consider compact $U^\kappa(1)$ gauge theory in 3+1D with the
$2\pi$-quantized topological term ${\sum_{I, J
=1}^\kappa\frac{K_{IJ}}{4\pi}\int_{M^4}F^I\wedge F^J}$. At energies below the
gauge charges' gaps but above the monopoles' gaps, this field theory has an
emergent ${\mathbb{Z}_{k_1}^{(1)}\times\mathbb{Z}_{k_2}^{(1)}\times\cdots}$
1-symmetry, where $k_i$ are the diagonal elements of the Smith normal form of
$K$ and $\mathbb{Z}_{0}^{(1)}$ is regarded as $U(1)^{(1)}$. In the
$U^\kappa(1)$ confined phase, the boundary's IR properties are described by
Chern-Simons field theory and has a
${\mathbb{Z}_{k_1}^{(1)}\times\mathbb{Z}_{k_2}^{(1)}\times\cdots}$ 1-symmetry
that can be anomalous. To show these results, we develop a bosonic lattice
model whose IR properties are described by this field theory, thus acting as
its UV completion. The lattice model in the aforementioned limit has an exact
${\mathbb{Z}_{k_1}^{(1)}\times\mathbb{Z}_{k_2}^{(1)}\times\cdots}$ 1-symmetry.
We find that a gapped phase of the lattice model, corresponding to the confined
phase of the $U^\kappa(1)$ gauge theory, is a symmetry protected topological
(SPT) phase for the
${\mathbb{Z}_{k_1}^{(1)}\times\mathbb{Z}_{k_2}^{(1)}\times\cdots}$ 1-symmetry,
whose SPT invariant is ${e^{i\pi\sum_{I, J}K_{IJ}\int B_I\smile
B_J+B_I\underset{1}{\smile} d B_J}e^{i\pi\sum_{I< J}K_{IJ}\int d
B_I\underset{2}{\smile}d B_J}}$. Here, the background 2-cochains $B_I$ satisfy
${d B_I=\sum_I B_{I}K_{IJ} = 0}$ mod $1$ and describe the symmetry twist of the
${\mathbb{Z}_{k_1}^{(1)}\times\mathbb{Z}_{k_2}^{(1)}\times\cdots}$ 1-symmetry.
We apply this general result to a few examples with simple $K$ matrices. We
find the non-trivial SPT order in the confined phases of these models and
discuss its classifications using the fourth cohomology group of the
corresponding 2-group.
