Vielbein to the Rescue?
  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.
