Massless spin 2 interacting with massive higher spins in d=3

TL;DR

This paper explores how massless spin 2 fields interact with massive higher-spin fermions in three dimensions, identifying possible interaction deformations and formulating corresponding Lagrangians.

Contribution

It systematically classifies all possible deformations of massive fermion equations in a massless spin 2 background and constructs their Lagrangian formulations.

Findings

Identified three linearly independent interaction solutions.

One solution corresponds to standard gravitational interactions.

Reconstructed Lagrangian formulations for all three cases.

Abstract

In this paper we consider massless spin 2 interacting with the massive arbitrary spin fermions in d=3. First of all, we study all possible deformations for the massive fermion unfolded equations in the massless spin 2 background. We find three linearly independent solutions one of which corresponds to the standard gravitational interactions. Then for all three cases we reconstruct appropriate Lagrangian formulation.