Unitarity Check in Gravitational Higgs Mechanism

TL;DR

This paper demonstrates that gravitational Higgs theories are equivalent to effective field theories of massive gravity and require similar adjustments to avoid ghosts, with the ghost presence being independent of the parametrization.

Contribution

It establishes the equivalence between gravitational Higgs theories and effective field theories of massive gravity, clarifying the conditions to avoid ghosts.

Findings

Gravitational Higgs theories are equivalent to massive gravity EFTs.

Ghost avoidance requires similar Lagrangian adjustments in both frameworks.

Ghost presence is independent of the parametrization used.

Abstract

The effective field theory of massive gravity had long been formulated in a generally covariant way arXiv:hep-th/0210184. Using this formalism, it has been found recently that there exists a class of massive nonlinear theories that are free of the Boulware-Deser ghosts, at least in the decoupling limit arXiv:1007.0443. In this work we study other recently proposed models that go under the name of "gravitational Higgs theories" arXiv:1002.3877, arXiv:1008.5132. We show that these models, although seemingly different from the effective field theories of massive gravity, are in fact equivalent to them. Furthermore, based on the results obtained in the effective field theory approach, we conclude that the gravitational Higgs theories need the same adjustment of the Lagrangian to avoid the ghosts. We also show the equivalence between the noncovariant mode decomposition used in the Higgs theories, and the covariant St\"uckelbergization adopted in the effective field theories, thus, proving that the presence or absence of the ghost is independent of the parametrization used in either theory.