Ghost free Massive Gravity in the St\"uckelberg language

TL;DR

This paper demonstrates how ghost-free massive gravity can be formulated in the St"uckelberg language beyond the decoupling limit, revealing the nonperturbative origin of the ghost-eliminating constraint.

Contribution

It establishes the consistency of ghost-free massive gravity in the St"uckelberg formalism beyond the decoupling limit without field redefinitions.

Findings

The constraint for removing the BD ghost arises nonperturbatively.

Vanishing Hessian determinant guarantees ghost absence.

Subtlety in deriving the constraint overlooked in previous work.

Abstract

Massive Gravity in four dimensions has been shown to be free of the Boulware-Deser (BD) ghost in the ADM language for a specific choice of mass terms. We show here how this is consistent with the St\"uckelberg language beyond the decoupling limit, and how the constraint required to remove the BD ghost arises in this framework nonperturbatively, without the use of field redefinitions. We emphasize a subtlety in obtaining this constraint, that has been overlooked in previous literature. In both the ADM and St\"uckelberg formalisms the vanishing of the determinant of a Hessian guarantees the absence of the BD ghost.