On gravitational interactions for massive higher spins in AdS3

In this paper we investigate gravitational interactions of massive higher spin fields in three dimensional AdS space with arbitrary value of cosmological constant including flat Minkowski space. We use the frame-like gauge description for such massive fields adapted to the three-dimensional case. First, we carefully analyze the procedure of switching on gravitational interactions in the linear approximation in the example of a massive spin-3 field and then proceed with the generalization to the case of an arbitrary integer spin field. As a result we construct a cubic interaction vertex linear in a spin-2 field and quadratic in a higher spin field on the AdS₃ background. As in the massless case the vertex does not contain any higher derivative corrections to the Lagrangian and/or gauge transformations. Thus, even after switching on gravitational interactions, one can freely consider any massless or partially massless limits as well as the flat one.