Massive gauge bosons from the conservation of topological winding numbers

TL;DR

This paper explores how topological winding numbers in a specific gauge theory lead to the emergence of massive gauge bosons when the theory is confined to small distances relative to the manifold's radii.

Contribution

It derives an effective theory showing that topological conservation laws induce mass for gauge bosons in a U(1) x SU(2) gauge theory on S^1 x S^3.

Findings

Gauge bosons become massive due to topological winding conservation.

Effective theory valid at small distances compared to sphere radii.

Topological constraints lead to mass generation in non-abelian gauge theories.

Abstract

We consider a U(1) x SU(2) gauge theory on the four-dimensional manifold S^1 x S^3. If we make the assumption that only gauge transformations connected to the identity are allowed, the winding numbers of U(1) around S^1 and of SU(2) around S^3 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.