Gravitational mass generation and consistent non-minimal couplings: cubics and quartics of a massive vector

TL;DR

This paper explores a novel approach to generate gauge-invariant mass for vector fields coupled to gravity, introducing consistent cubic and quartic interactions and offering a geometric interpretation.

Contribution

It presents a modified Noether procedure to derive gauge-invariant mass and interactions for a vector field coupled to gravity, extending previous methods.

Findings

Derived gauge-invariant mass for vector fields

Established consistent cubic and quartic interactions

Proposed a geometric interpretation of the vector field

Abstract

An attempt to evade the strict uniqueness of consistent interactions involving spin-2 particles is made by modifying the Noether procedure from the outset. A vector field is introduced, coupled to a graviton already at the level of quadratic mixing. The byproduct is a gauge-invariant mass for the vector and novel consistent interactions, here derived and tested up to quartic order. A simple geometric interpretation of the vector field appears possible.