On electromagnetic interaction of massive spin-2 particle

TL;DR

This work develops a gauge-invariant framework for free massive particles with arbitrary integer spin by introducing a tower of lower-spin fields, ensuring the massless limit yields a sum of spins $s, s-1, \ldots, 0$. It then applies this framework to the electromagnetic interaction of a massive spin-$2$ particle, first in linear approximation and then in a constant homogeneous electromagnetic field across arbitrary space-time dimensions, deriving explicit gauge-invariant couplings and a full Lagrangian up to fourth order in the field strength. The main contributions include a practical, dimension-independently valid construction of gauge-invariant Lagrangians for massive high-spin fields and explicit spin-$2$ electromagnetic couplings with determined coefficients, illuminating a path toward consistent high-spin interactions in flat space and connecting with KK/string-inspired approaches. Overall, the paper provides a systematic method to analyze and extend gauge-invariant interactions for massive higher-spin fields beyond the massless regime.

Abstract

In this work we construct a gauge invariant description of free massive particle with an arbitrary integer spin. Such description allows one to investigate the problem of consistent interactions for massive high spin particles using the requirement that the whole interaction Lagrangian must be gauge invariant. As a first example of such approach, we consider the case of electromagnetic interaction of massive spin-2 particle: a linear approximation in a case of the arbitrary field and a full theory for the homogeneous electromagnetic field in the space-time of any dimensionality.