Complete Decoupling Limit of Ghost-free Massive Gravity

TL;DR

This paper derives the complete decoupling limit of ghost-free massive gravity, explicitly including interactions of helicity-1 and helicity-0 modes using a vierbein formulation, clarifying the equations of motion and symmetry conditions.

Contribution

It provides a fully resummed expression for the helicity-1 interactions in the decoupling limit using vierbeins, enhancing understanding of the theory's structure.

Findings

Explicit form of the decoupling limit including all interactions

Resummed expression for helicity-1 field interactions

Clarification of the vierbein and metric equivalence conditions

Abstract

We present the complete form of the decoupling limit of ghost-free massive gravity with a Minkowski reference metric, including the full interactions of the helicity-1 and helicity-0 modes of the massive spin-2 field. While in the metric language the square root structure of the mass terms makes it difficult to find a simple way to write down the interactions, we show that using the vierbein formulation of massive gravity, including Stueckelberg fields for both diffeomorphism and local Lorentz symmetries, we can find an explicitly resummed expression for the helicity-1 field interactions. We clarify the equations of motion for the Lorentz Stueckelberg fields and how these generate the symmetric vierbein condition which guarantees equivalence between the vierbein and metric formulations of massive gravity.