Generalized SU(2) Proca Theory

TL;DR

This paper develops a comprehensive framework for the generalized SU(2) Proca theory, extending Abelian vector Galileons to non-Abelian gauge fields, with potential applications in cosmology such as gauge-driven inflation.

Contribution

It systematically constructs all relevant Lagrangians up to six Lorentz indices for the non-Abelian case and identifies those with healthy dynamics propagating three degrees of freedom.

Findings

Identified independent Lagrangians with healthy longitudinal modes.

Extended the theory to curved spacetime and higher orders.

Connected the theory to multi-Galileon dynamics.

Abstract

Following previous works on generalized Abelian Proca theory, also called vector Galileon, we investigate the massive extension of an SU(2) gauge theory, i.e., the generalized SU(2) Proca model, which could be dubbed non-Abelian vector Galileon. This particular symmetry group permits fruitful applications in cosmology such as inflation driven by gauge fields. Our approach consists in building, in an exhaustive way, all the Lagrangians containing up to six contracted Lorentz indices. For this purpose, and after identifying by group theoretical considerations all the independent Lagrangians which can be written at these orders, we consider the only linear combinations propagating three degrees of freedom and having healthy dynamics for their longitudinal mode, i.e., whose pure St\"uckelberg contribution turns into the SU(2) multi-Galileon dynamics. Finally, and after having considered the curved space-time expansion of these Lagrangians, we discuss the form of the theory at all subsequent orders.