The Higgs sector of gravitational gauge theories

Abstract

Gravitational gauge theories with de Sitter, Poincare and affine symmetry group are investigated under the aspect of the breakdown of the initial symmetry group down to the Lorentz subgroup. We review the theory of spontaneously broken de Sitter gravity by Stelle and West and apply a similar approach to the case of the Poincare and affine groups. Especially, we find that the groundstate of the metric affine theory leads to the determination of the Lorentzian signature of the metric in the groundstate. We show that the Higgs field remains in its groundstate, i.e., that the metric will have Lorentzian signature, unless we introduce matter fields that explicitely couple to the symmetric part of the connection. We also show that some features, like the necessity of the introduction of a dilaton field, that seem artificial in the context of the affine theory, appear most natural if the gauge group is taken to be the special linear group in five dimensions. Finally, we present an alternative model which is based on the spinor representation of the Lorentz group and is especially adopted to the description of spinor fields in a general linear covariant way, without the use of the infinite dimensional representations which are usually considered to be unavoidable.