Symmetry breaking in Kaluza-Klein theories

Abstract

A new mechanism of symmetry breaking in Kaluza-Klein theories with elementary gauge fields is proposed. In order to implement it, a multiplet of scalar fields with a potential term (as in the usual Higgs mechanism in four dimensions) must be introduced. A general solution of the classical equations of motion is given with the internal manifold being a deformed N-sphere with isometry O(N). The particular six-dimensional case (deformed S2) is discussed in detail. It is shown that in the lowest order of perturbation theory in the deformation parameter epsilon the solution can be made classically stable. The local O(3)*U(1) gauge symmetry is broken to a U(1) subgroup of O(3) and there is a corresponding massless vector boson. The remaining vector bosons acquire small masses of order epsilon 2.