Phases of Theories with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mm

We analyze the phases of theories having a microscopic Z_{N} 1-form symmetry, starting with a topological BF theory and deforming it so that only the microscopic symmetry is preserved. These theories have a well-defined notion of confinement, prototypical examples being pure SU(N) and Z_{N} gauge theories in the continuum and on the lattice. Our analysis shows that the 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 Coulomb phase. We construct a Z_{N} lattice gauge theory with a deformation that, surprisingly, produces up to (N-1) photons. We give an interpretation of these findings in terms of the behaviors of two competing drivers of confinement-magnetic monopoles and center vortices-and conclude that proliferation of center vortices is necessary but insufficient for confinement, while proliferation of magnetic monopoles is both necessary and sufficient.