Gravitational Interaction of Higher Spin Massive Fields and String Theory

TL;DR

This paper investigates the consistent coupling of higher spin massive fields, especially spin 2, to gravity, exploring conditions for causality and degrees of freedom, and deriving related equations from string theory.

Contribution

It provides a detailed analysis of the conditions for consistent higher spin field coupling to gravity and links field theory results with string theory equations.

Findings

Existence of two consistent coupling scenarios: on specific manifolds and in arbitrary spacetime with curvature series.

Derivation of background spin 2 field equations from string theory via quantum Weyl invariance.

Consistency conditions ensure correct degrees of freedom and causal propagation.

Abstract

We discuss the problem of consistent description of higher spin massive fields coupled to external gravity. As an example we consider massive field of spin 2 in arbitrary gravitational field. Consistency requires the theory to have the same number of degrees of freedom as in flat spacetime and to describe causal propagation. By careful analysis of lagrangian structure of the theory and its constraints we show that there exist at least two possibilities of achieving consistency. The first possibility is provided by a lagrangian on specific manifolds such as static or Einstein spacetimes. The second possibility is realized in arbitrary curved spacetime by a lagrangian representing an infinite series in curvature. In the framework of string theory we derive equations of motion for background massive spin 2 field coupled to gravity from the requirement of quantum Weyl invariance. These equations appear to be a particular case of the general consistent equations obtained from the field theory point of view.