Massive gauge bosons from the conservation of topological winding numbers
Abstract
We consider a U(1) x SU(2) gauge theory on the four-dimensional manifold S1 x S3. If we make the assumption that only gauge transformations connected to the identity are allowed, the winding numbers of U(1) around S1 and of SU(2) around S3 become topological conserved quantities. We derive the effective theory for non-trivial winding numbers if all distances are small compared to the radii of the spheres. In the non-abelian case the gauge bosons become massive.
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