Gravitational cubic interactions for a massive mixed symmetry gauge field

TL;DR

This paper extends the construction of cubic gravitational interactions from massless to massive mixed symmetry gauge fields in (A)dS spaces, using a frame-like gauge invariant approach, and explores the differences in interaction possibilities across spacetime geometries.

Contribution

It introduces a method to describe massive mixed symmetry fields in (A)dS spaces and analyzes their gravitational interactions, highlighting the impossibility of such interactions for massless fields in dS space.

Findings

Massive mixed symmetry fields can have cubic gravitational interactions in (A)dS.

Massless fields in dS space cannot have gravitational interactions.

The approach works in flat Minkowski space as well.

Abstract

In a recent paper arXiv:1107.1872 cubic gravitational interactions for a massless mixed symmetry field in AdS space have been constructed. In the current paper we extend these results to the case of massive field. We work in a Fradkin-Vasiliev approach and use frame-like gauge invariant description for massive field which works in (A)dS spaces with arbitrary values of cosmological constant including flat Minkowski space. In this, massless limit in AdS space coincides with the results of arXiv:1107.1872 while we show that it is impossible to switch on gravitational interaction for massless field in dS space.