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.
Highlights
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 show that the interactions of the scalar Higgs field itself enjoys Galileonic symmetries, and that the Higgs-Goldstone boson system assembles into a specific bi-Galileon combination
We showed that the Lagrangian controlling the would-be Goldstone boson of this theory obtains a Galileon structure in an appropriate decoupling limit
Summary
We discuss a Higgs mechanism that spontaneously breaks an abelian symmetry, in such a way to generate a vector mass term and the class of derivative vector self-interactions studied in [7, 8]. The couplings that govern those interactions are fixed by the mechanism of symmetry breaking and gauge invariance, and are suppressed by a mass scale corresponding to the vector mass mA to appropriate powers Notice that all these new higher dimensional interactions are derived from our initial Lagrangian, and are ghost-free since the associated equations of motion contain at most two space-time derivatives. In our Higgs set-up, we can do one step further: we show that in this decoupling limit, do the Goldstone self-interactions preserve Galileon invariance by themselves, but in addition they acquire new derivative couplings with the Higgs field h These automatically preserve the Galileon symmetry by assembling into bi-Galileon combinations. We hope to return to this subject with a separate detailed publication
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