A Higgs Mechanism for Vector Galileons

TL;DR

This paper introduces a Higgs mechanism for vector Galileons, enabling spontaneous gauge symmetry breaking and generating ghost-free scalar-vector interactions, with potential cosmological applications.

Contribution

It develops a formalism to construct gauge-symmetry-breaking vector theories via a Higgs mechanism, extending to non-abelian symmetries and connecting with scalar bi-Galileon interactions.

Findings

Generated ghost-free scalar-vector interactions.

Reduced to scalar bi-Galileon interactions in a decoupling limit.

Extended formalism from abelian to non-abelian gauge symmetries.

Abstract

Vector theories with non-linear derivative self-interactions that break gauge symmetries have been shown to have interesting cosmological applications. In this paper we introduce a way to spontaneously break the gauge symmetry and construct these theories via a Higgs mechanism. In addition to the purely gauge field interactions, our method generates new ghost-free scalar-vector interactions between the Higgs field and the gauge boson. We show how these additional terms are found to reduce, in a suitable decoupling limit, to scalar bi-Galileon interactions between the Higgs field and Goldstone bosons. Our formalism is first developed in the context of abelian symmetry, which allows us to connect with earlier work on the extension of the Proca action. We then show how this formalism is straightforwardly generalised to generate theories with non-abelian symmetry.