Equations of Motion for Massive Spin 2 Field Coupled to Gravity

We derive consistent equations of motion for the massive spin two field interacting with gravity and massless scalar dilaton field in arbitrary spacetime dimension. From the field theoretical point of view we describe the most general classical action with non-minimal couplings and find the most general gravitational background on which this action describes a theory consistent with the flat space limit and causal. We show also that the massive spin two field can be consistently described in arbitrary background by means of either non-lagrangian equations or the lagrangian ones representing an infinite series in the inverse mass square. 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 explicit form of these effective equations of motion coincides with the general form of consistent equations derived in field theory.