New Kinetic Terms for Massive Gravity and Multi-gravity: A No-Go in Vielbein Form

TL;DR

This paper investigates new kinetic terms in the vielbein formulation of massive gravity and finds that they introduce additional degrees of freedom that are strongly coupled and non-ghostly, supporting the uniqueness of Einstein-Hilbert as the kinetic term.

Contribution

The study demonstrates that alternative kinetic terms in vielbein massive gravity lead to strongly coupled extra degrees of freedom, confirming the Einstein-Hilbert term's uniqueness.

Findings

New degrees of freedom are associated with Lorentz transformations in vielbein formulation.

These degrees of freedom are strongly coupled and not part of the spin-2 multiplet.

The results support the Einstein-Hilbert term as the unique kinetic term for massive gravity.

Abstract

We reconsider the possibility of a class of new kinetic terms in the first order (vielbein) formulation of massive gravity and multi-gravity. We find that new degrees of freedom emerge which are not associated with the Boulware--Deser ghost and are intrinsic to the vielbein formulation. These new degrees of freedom are associated with the Lorentz transformations which encode the additional variables contained in the vielbein over the metric. Although they are not guaranteed to be ghostly, they are nevertheless infinitely strongly coupled on Minkowski spacetime and are not part of the spin-2 multiplet. Hence their existence implies the uniqueness of the Einstein--Hilbert term as the kinetic term for a massive graviton.