New Bi-Gravity from New Massive Gravity

Using the action of three dimensional New Massive Gravity (NMG) we construct a new bi-gravity in three dimensions. This can be done by promoting the rank two auxiliary field appearing in the expression of NMG's action into a dynamical field. We show that small fluctuations around the AdS vacuum of the model are non-tachyonic and ghost free within certain range of the parameters of the model. We study central charges of the dual field theory and observe that in this range they are positive too. This suggests that the proposed model might be a consistent three dimensional bi-gravity.