Covariantised Vector Galileons

TL;DR

This paper investigates the coupling of vector Galileons with gravity, establishing conditions to avoid ghosts, and explores a Higgs mechanism for generating these vector fields with a consistent covariant approach.

Contribution

It provides a detailed analysis of ghost-free conditions for vector Galileons coupled to gravity and proposes a Higgs mechanism for their generation with a covariant formulation.

Findings

Conditions for ghost-free vector Galileons with gravity

Indications of a 'beyond Horndeski' vector theory avoiding ghosts

A covariant Higgs mechanism for vector Galileons

Abstract

Vector Galileons are ghost-free systems containing higher derivative interactions of vector fields. They break the vector gauge symmetry, and the dynamics of the longitudinal vector polarizations acquire a Galileon symmetry in an appropriate decoupling limit in Minkowski space. Using an ADM approach, we carefully reconsider the coupling with gravity of vector Galileons, with the aim of studying the necessary conditions to avoid the propagation of ghosts. We develop arguments that put on a more solid footing the results previously obtained in the literature. Moreover, working in analogy with the scalar counterpart, we find indications for the existence of a `beyond Horndeski' theory involving vector degrees of freedom, that avoids the propagation of ghosts thanks to secondary constraints. In addition, we analyze a Higgs mechanism for generating vector Galileons through spontaneous symmetry breaking, and we present its consistent covariantisation.