Bosonization of fermions coupled to topologically massive gravity

We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d = 3 space-time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy-momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2 + 1 Abelian and non-Abelian bosonization in flat space-time.