On massive spin 2 interactions

TL;DR

The paper develops a gauge-invariant framework for analyzing interactions of a massive spin-2 particle in $(A)dS_d$ backgrounds, covering self-interactions, matter couplings to spins $0,1,\tfrac12$, and gravity. Using a linearized, two-derivative cubic-vertex approach, it shows that self-interactions generally exist in $d\ge 3$ only if the vector Goldstone field $A_\mu$ has a noncanonical $\xi_\mu$ transformation, with a special partially massless sector at $d=4$ ($c_0=0$). It reveals an intrinsic ambiguity between flat-space and massless limits in matter couplings (via $m/c_0$-type dependencies) and identifies precise constraints for couplings to gravity, including the impossibility of a two-massless-one-massive cubic vertex and the existence of covariant vertices with two massive fields and any number of massless gravitons. The results, valid at linear order and independent of the presence of other fields, point to the necessity of higher-derivative terms or extra fields for full non-linear completion and offer insights into the structure of massive gravity and partially massless theories in curved backgrounds.

Abstract

In this paper we use a constructive approach based on gauge invariant description of massive high spin particles for investigation of possible interactions of massive spin 2 particle. We work with general case of massive spin 2 particle living in constant curvature $(A)dS_d$ background, which allows us carefully consider all flat space, massless or partially massless limits. In the linear approximation (cubic terms with no more than two derivatives in the Lagrangians and linear terms with no more than one derivative in gauge transformations) we investigate possible self-interaction, interaction with matter (i.e. spin 0, 1 and 1/2 particles) and interaction with gravity.