  We analyze the phases of theories which only have a microscopic
$\mathbb{Z}_N$ 1-form symmetry, starting with a topological BF theory and
deforming it in accordance with microscopic symmetry. These theories have a
well-defined notion of confinement. Prototypical examples are pure $SU(N)$
gauge theories and $\mathbb{Z}_N$ lattice gauge theories. Our analysis shows
that the only generic phases are in $d=2$, only the confined phase; in $d=3$,
both the confined phase and the topological BF phase; and in $d=4$, the
confined phase, the topological BF phase, and a phase with a massless photon.
We construct a $\mathbb{Z}_N$ lattice gauge theory with a deformation which,
surprisingly, produces up to $(N-1)$ photons. We give an interpretation of
these findings in terms of two competing pictures of confinement --
proliferation of monopoles and proliferation of center vortices -- and conclude
that the proliferation of center vortices is a necessary but insufficient
condition for confinement, while that of monopoles is both necessary and
sufficient.
