  We study a three-dimensional abelian lattice model in which the analogue of a
theta term can be defined. This term is defined by introducing a neutral scalar
field and its effect is to couple magnetic monopoles to the scalar field and
vortices to the gauge field. An interesting feature of this model is the
presence of an exact duality symmetry that acts on a three parameter space. It
is shown that this model has an interesting phase structure for non-zero values
of theta. In addition to the usual confinement and vortex phases there are
phases in which loops with composite charges condense. The presence of novel
point like excitations also alters the physical properties of the system.
