Symmetry Breaking of Gauge Theories via Internal Space Dynamics

TL;DR

This paper proposes a geometric mechanism for gauge symmetry breaking in higher-dimensional theories, where internal space dynamics induce mass for gauge bosons, akin to a geometric Higgs mechanism.

Contribution

It introduces a novel geometric approach to gauge symmetry breaking via internal space dynamics in Kaluza-Klein theories, including explicit mass calculations for gauge bosons.

Findings

Broken gauge bosons acquire mass after internal manifold transitions

Internal space dynamics can induce partial gauge symmetry breaking

A Higgs-like mechanism may operate through geometric transitions

Abstract

In this paper, I explain how gauge symmetry can be broken in a geometric way, \`{a} la Kaluza-Klein. In higher dimensional gravitational theories, one usually considers the extra dimensions to be ``frozen'' in time. However, the internal manifold is actually a dynamic entity. For example, its metric can change even if one expects its topological properties to be invariant. It is conceivable then, that at an earlier epoch the internal manifold made a geometric transition from say a maximally symmetric metric space to a less symmetric one. We know in a Kaluza-Klein reduction scheme, the massless gauge bosons are associated with the Killing vectors of the internal manifold. After the transition of the internal manifold, the gauge bosons associated with the broken Killing isometries will pick up a mass thereby breaking the gauge invariance partially. In this paper, I explore this idea, work out the mass of broken gauge bosons for some simple examples, and also point out how a mechanism similar to that of Higgs may be at work.