The Boulware-Deser Mode in 3d First-Order Massive Gravity

Massive gravity in three dimensions accepts several different formulations. Recently, the three-dimensional bigravity de Rham-Gabadadze-Tolley (dRGT) model in first-order form, Zwei-Dreibein gravity, was considered by Bergshoeff et al., and it was argued that the Boulware-Deser mode is killed by extra constraints. We revisit this assertion and conclude that there are sectors on the space of initial conditions, or subsets of the most general such model, where this mode is absent. But, generically, the theory does carry 3 degrees of freedom, and thus the Boulware-Deser mode is still active. Our results also sheds light on the equivalence between metric and vierbein formulations of the dRGT model.