Equations of motion for massive spin 2 field coupled to gravity

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and m assless scalar dilaton fields in arbitrary spacetime dimension. From the fi eld theoretical point of view we consider a general classical action with n on-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit, in th e case of pure gravitational background all field components propagate caus ally, We show also that the massive spin two field can be consistently desc ribed in arbitrary background by means of the lagrangian representing an in finite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requi rement of quantum Weyl invariance of the corresponding two-dimensional sigm a-model. In the lowest order in alpha' we demonstrate that these effective equations of motion coincide with consistent equations derived in field the ory. (C) 2000 Elsevier Science B.V. All rights reserved.