(2+1)-dimensional interacting models of two massless spin-2 fields as bi-gravity models

We propose new group-theoretical (Chern-Simons) formulations for the bi-metric theory of gravity in (2+1)-dimensional (3D) spacetime which describe two interacting massless spin-2 fields. Our models have been formulated in terms of two dreibeins rather than two metrics. We obtain our first Chern-Simons gravity model by gauging mixed AdS-AdS Lie algebra and show that it has a 2d conformal field theory (CFT) at the boundary of the anti de Sitter (AdS) solution. We show that the central charge of the dual CFT is proportional to the mass of the AdS solution. Our second Chern-Simons gravity model is obtained by gauging AdS Lie bialgebra and has a new black hole solution with two curvature singularities and two horizons..