Bosonization of fermions coupled to topologically massive gravity

We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3d=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+12+1 Abelian and non-Abelian bosonization in flat space–time.