On Consistent Equations for Massive Spin-2 Field Coupled to Gravity in String Theory

TL;DR

This paper derives consistent equations of motion for a massive spin-2 field coupled to gravity using both field theory and string theory approaches, highlighting the conditions for consistency and the equivalence of results.

Contribution

It provides the most general classical action with non-minimal couplings for the massive spin-2 field and shows the equivalence of string theory and field theory equations of motion.

Findings

Derived the most general classical action with non-minimal couplings.

Identified conditions for consistent coupling in arbitrary backgrounds.

Showed string theory equations match field theory results at lowest order.

Abstract

We investigate the problem of derivation of consistent equations of motion for the massive spin 2 field interacting with gravity within both field theory and string theory. In field theory we derive the most general classical action with non-minimal couplings in arbitrary spacetime dimension, find the most general gravitational background on which this action describes a consistent theory and generalize the analysis for the coupling with background scalar dilaton field. We show also that massive spin 2 field allows in principle consistent description in arbitrary background if one builds its action in the form of an infinite series in the inverse mass square. Using sigma-model description of string theory in background fields we obtain in the lowest order in $\alpha'$ the explicit form of effective equations of motion for the massive spin 2 field interacting with gravity from the requirement of quantum Weyl invariance and demonstrate that they coincide with the general form of consistent equations derived in field theory.