Spontaneous symmetry breaking and gravity

Abstract

Gravity is usually considered to be irrelevant as far as the physics of elementary particles is concerned and, in particular, in the context of the spontaneous symmetry breaking (SSB) mechanism. We describe a version of the SSB mechanism in which gravity plays a direct role. We work in the context of diffeomorphism invariant gauge theories, which exist for any non-abelian gauge group G, and which have second order in derivatives field equations. We show that any (non-trivial) vacuum solution of such a theory gives rise to an embedding of the group SU(2) into G, and thus breaks G down to SU(2) times its centralizer in G. The components of the connection charged under SU(2) can then be seen to describe gravitons, with the SU(2) itself playing the role of the chiral half of the Lorentz group. Components charged under the centralizer describe the usual Yang-Mills gauge bosons. The remaining components describe massive particles. This breaking of symmetry explains (in the context of models considered) how gravity and Yang-Mills can come from a single underlying theory while being so different in the physics they describe. Further, varying the vacuum solution, and thus the embedding of SU(2) into G, one can break the Yang-Mills gauge group as desired, with massless gauge bosons of one vacuum acquiring mass in another. There is no Higgs field in our version of the SSB mechanism, the only variable is a connection field. Instead of the symmetry breaking by a dedicated Higgs field pointing in some direction in the field space, our theories break the symmetry by choosing how the group of "internal" gauge rotations of gravity (the chiral half of the Lorentz group) sits inside the full gauge group.