Consistent equations for massive spin-2 field coupled to gravity in stringtheory

We investigate the problem of derivation of consistent equations of motion for the massive spin 2 field interacting with gravity within both field the ory and string theory. In field theory we derive the most general classical action with non-minimal couplings in arbitrary spacetime dimension, find t he most general gravitational background on which this action describes a c onsistent theory and generalize the analysis for the coupling with backgrou nd scalar dilaton field. We shaw also that massive spin 2 field allows in p rinciple consistent description in arbitrary background if one builds its a ction in the form of an infinite series in the inverse mass square. Using s igma-model description of string theory in background fields we obtain in t he lowest order in alpha' the explicit form of effective equations of motio n for the massive spin 2 field interacting with gravity from the requiremen t of quantum Weyl invariance and demonstrate that they coincide with the ge neral form of consistent equations derived in field theory. (C) 1999 Publis hed by Elsevier Science B.V. All rights reserved.