Symmetry breaking of gauge theories down to Abelian sub-groups

Abstract

I re-derive the lowest order effective Lagrangian for electro-weak symmetry breaking without the use of Goldstone's theorem for spontaneously broken global symmetries and without the assumption of a custodial symmetry. I consider the breaking of a local symmetry with gauge group G down to an Abelian sub-group K and construct a gauge-invariant functional with one free parameter v, such that v=0 corresponds to a gauge theory with gauge group G, while v --> infinity corresponds to a gauge theory with gauge group K.