Vielbein to the Rescue?

TL;DR

This paper examines non-minimal matter couplings in massive gravity and multi-gravity, demonstrating that the Boulware-Deser ghost reemerges beyond the decoupling limit in both metric and vielbein formulations, especially when the symmetric vielbein condition is violated.

Contribution

It shows that the ghost is always present beyond the decoupling limit in higher dimensions, regardless of the formulation, challenging previous claims of ghost-free conditions in vielbein formulations.

Findings

Ghost reappears beyond the decoupling limit in higher dimensions.

Metric and vielbein formulations share identical ghost-free decoupling limits.

Ghost presence persists when the symmetric vielbein condition is broken.

Abstract

Non-minimal matter couplings have recently been considered in the context of massive gravity and multi-gravity. These couplings are free of the Boulware-Deser ghost in the decoupling limit and can thus be considered within an Effective Field Theory setup. Beyond the decoupling limit the ghost was shown to reemerge in the metric formulation of the theory. Recently it was argued that this pathology is absent when formulated in terms of unconstrained vielbeins. We investigate this possibility and show that the Boulware-Deser ghost is always present beyond the decoupling limit in any dimension larger than two. We also show that the metric and vielbein formulations have an identical ghost-free decoupling limit. Finally we extend these arguments to more generic multi-gravity theories and argue that for any dimension larger than two a ghost is also present in the vielbein formulation whenever the symmetric vielbein condition is spoiled and the equivalence with the metric formulation is lost.