Equations of Motion for Massive Spin 2 Field Coupled to Gravity

TL;DR

This paper studies the equations of motion for a massive spin 2 field coupled to gravity, ensuring consistency and causality in various backgrounds, and connects string theory results with field theory formulations.

Contribution

It derives consistent equations of motion for a massive spin 2 field in arbitrary backgrounds, linking string theory and field theory approaches.

Findings

Massive spin 2 field propagates causally in pure gravitational backgrounds.

Equations of motion derived from string theory match those from field theory at lowest order.

The theory remains consistent with the flat space limit under certain background conditions.

Abstract

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two dimensional sigma-model. In the lowest order in $\alpha'$ we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.