Spontaneous Symmetry Breaking for Massive Spin-2 Interacting with Gravity

TL;DR

The paper addresses constructing a consistent action for a massless graviton interacting with a massive spin-2 field by coupling gravity to a gauge theory based on $SP(4)$ that is spontaneously broken to $SL(2,C)$ via a Higgs multiplet. The authors derive a metric-independent action with a Goldstone sector and a mixing term to the metric, then analyze the model in unitary and non-unitary gauges to reveal the six degrees of freedom: two tensor helicities, two vector helicities from the Goldstone multiplet, and two scalar modes. They show that the propagators are well-behaved and that the problematic FP ghost can be controlled by a high-energy cutoff, with a smooth $m o0$ limit in the non-unitary gauge. The work also outlines possible symmetric generalizations (e.g., $SP(4) imes SP(4)$) for a dual-metric or brane-inspired interpretation and sets the stage for further explicit massless-limit computations.

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.