Spontaneous Symmetry Breaking for Massive Spin-2 Interacting with Gravity

TL;DR

This paper introduces a model where a massless graviton interacts with a massive tensor field through spontaneous symmetry breaking, resulting in well-behaved propagators and a clear identification of degrees of freedom.

Contribution

It proposes a novel action coupling a massless graviton to a massive tensor via an SP(4) gauge theory with spontaneous symmetry breaking, clarifying the degrees of freedom involved.

Findings

Propagators are well-behaved unlike previous tensor-tensor systems.

Degrees of freedom include tensor, vector, and scalar helicities.

Model achieves consistent massive spin-2 interaction with gravity.

Abstract

An action for a massless graviton interacting with a massive tensor field is proposed. The model is based on coupling the metric tensor to an SP(4) gauge theory spontaneously broken to $SL(2,C)$. The symmetry breaking is achieved by using a Higgs multiplet containing a scalar field and a vector field related by a constraint. We show that in the non-unitary gauge and for the Fierz-Pauli form of the mass term, the six degrees of freedom of the massive tensor are identified with two tensor helicities, two vector helicities of the Goldstone vector, and two scalars present in the Goldstone multiplet. The propagators of this system are well behaved, in contrast to the system consisting of two tensors.