Interaction of higher spin massive fields with gravity in string theory

TL;DR

This paper reviews the derivation of consistent equations of motion for massive spin two fields interacting with gravity, connecting field theory and string theory approaches, and demonstrating their agreement at lowest order.

Contribution

It provides a unified derivation of the equations of motion for massive spin two fields in curved spacetime from both field theory and string theory perspectives.

Findings

Consistent causal propagation equations in vacuum Einstein spacetime.

String theory equations match field theory results at lowest order.

Lagrangian equations involve an infinite series in curvature.

Abstract

Derivations of consistent equations of motion for the massive spin two field interacting with gravity is reviewed. From the field theoretical point of view the most general classical action describing consistent causal propagation in vacuum Einstein spacetime is given. It is also shown that the massive spin two field can be consistently described in arbitrary background by means of lagrangian equations representing an infinite series in curvature. Within string theory equations of motion for the massive spin two field coupled to gravity is derived from the requirement of quantum Weyl invariance of the corresponding two dimensional sigma-model. In the lowest order in string length the effective equations of motion are demonstrated to coincide with the general form of consistent equations derived in field theory.