Proof of consistency of nonlinear massive gravity in the Stückelberg formulation

Abstract

We address some recent concerns about the absence of the Boulware–Deser ghost in the Stückelberg formulation of nonlinear massive gravity. First we provide general arguments for why any ghost analysis in the Stückelberg formulation has to agree with existing consistency proofs that have been carried out without using Stückelberg fields. We then demonstrate the absence of the ghost at the completely nonlinear level in the Stückelberg formulation of the minimal massive gravity action. The constraint that removes the ghost field and the associated secondary constraint that eliminates its conjugate momentum are computed explicitly, confirming the consistency of the theory in the Stückelberg formulation.