Supersymmetrizing Massive Gravity

TL;DR

This paper develops a supersymmetric extension of massive gravity by coupling four chiral superfields to supergravity, resulting in a model with a massive graviton, spin-3/2 fields, and a vector, breaking both diffeomorphism and supersymmetry spontaneously.

Contribution

It introduces a novel supersymmetrization of massive gravity using chiral superfields, linking scalar VEVs to the emergence of massive supermultiplets.

Findings

Spectrum includes a massive spin-2 field.

Presence of two massive spin-3/2 fields.

A massive vector field is also present.

Abstract

When four scalar fields with global Lorentz symmetry are coupled to gravity and take a vacuum expectation value breaking diffeomorphism invariance spontaneously, the graviton becomes massive. This model is supersymmetrized by considering four N=1 chiral superfields with global Lorentz symmetry. When the scalar components of the chiral multiplets z^A acquire a vacuum expectation value, both diffeomorphism invariance and local supersymmetry are broken spontaneously. The global Lorentz index A becomes identified with the space-time Lorentz index making the scalar fields z^A vectors and the chiral spinors psi^A spin-3/2 Rarita-Schwinger fields. The global supersymmetry is promoted to a local one using the rules of tensor calculus of coupling the N=1 supergravity Lagrangian to the four chiral multiplets. We show that the spectrum of the model in the broken phase consists of a massive spin-2 field, two massive spin-3/2 fields with different mass and a massive vector.