Abstract
Working within the path-integral framework we first establish a duality between the partition functions of two U(1) gauge theories with a theta term in d=4 space-time dimensions. Then, after a dimensional reduction to d=3 dimensions we arrive to the partition function of a U(1) gauge theory coupled to a scalar field with an action that exhibits a Dirac monopole solution. A subsequent reduction to d=2 dimensions leads to the partition function of a theory in which the gauge field decouples from two scalars which have non-trivial vortex-like solutions. Finally this d=2 partition function can be related to the bosonized version of the two-dimensional QED2 (Schwinger) model.
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