On spin 2 electromagnetic interactions

TL;DR

This work addresses whether massless spin-2 particles can electromagnetically couple without breaking gauge invariance in flat space. It develops a cubic three-derivative vertex for a 2-2-1 interaction, then reformulates the theory in a frame-like language and finally deforms it to (A)dS to restore gauge invariance at linear order. The main contributions are explicit Lagrangian terms and gauge transformations for the 2-2-1 vertex, a consistent frame-like construction, and concrete deformation coefficients that preserve invariance in (A)dS. The results show that minimal electromagnetic coupling for massless spin-2 is viable in curved backgrounds with non-minimal higher-derivative corrections, and they hint at a deeper link between massless AdS and massive flat-space theories.

Abstract

In this paper we (re)consider the problem of electromagnetic interactions for massless spin 2 particles and show that in $(A)dS$ spaces with non-zero cosmological constant it is indeed possible (at least in linear approximation) to switch on minimal electromagnetic interactions supplemented by third derivative non-minimal ones which are necessary to restore gauge invariance.