On gravitational interactions for massive higher spins in $AdS_3$

TL;DR

This paper develops a gauge-invariant framework for describing gravitational interactions of massive higher spin fields in three-dimensional $AdS_3$, constructing interaction vertices that remain consistent across massless, partially massless, and flat limits.

Contribution

It introduces a gauge-invariant cubic interaction vertex for massive higher spins in $AdS_3$, valid for arbitrary cosmological constant, with no higher derivative corrections.

Findings

Constructed a cubic interaction vertex linear in the graviton and quadratic in higher spins.

The vertex is free of higher derivatives, maintaining gauge invariance.

The framework applies to massless, partially massless, and flat limits.

Abstract

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 frame-like gauge description for such massive fields adopted to three-dimensional case. At first, we carefully analyze the procedure of switching on gravitational interactions in the linear approximation on the example of massive spin-3 field and then proceed with the generalization to the case of arbitrary integer spin field. As a result we construct a cubic interaction vertex linear in spin-2 field and quadratic in higher spin field on $AdS_3$ 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.