Dynamical gauge symmetry breaking as the casimir effect

Abstract

A new mechanism for dynamical gauge symmetry breaking is found in a class of higher dimensional theories. A system consisting of non-abelian gauge fields and fermions with minimal gauge interactions on a spacetime M 2 × S 2 is considered, where M n and S 2 are an n-dimensional Minkowski spacetime and a surface of a sphere, respectively. Full analysis is given for odd n. By integrating fermion fields first, we find that gauge symmetry is dynamically broken for n = 4 p + 3 ( p = 0, 1, 2…), provided that there exists a sufficiently heavy fermion. The phenomenon originates from a shift in fermion zero point energies due to compactness of the extra dimensional space S 2, being quite similar to the Casimir effect in electrodynamics.