Massive higher spin fields in curved spacetime and necessity of non-minimal couplings

TL;DR

This paper investigates the behavior of free massive higher spin fields in curved spacetime, emphasizing the necessity of non-minimal couplings to curvature, and derives specific conditions for spin 2 and discusses spin 3 cases.

Contribution

It provides a detailed analysis of non-minimal couplings for higher spin fields in curved spacetime, including explicit conditions for spin 2 and insights into spin 3.

Findings

Non-minimal couplings are necessary for higher spin fields in curved spacetime.

Derived specific conditions for spin 2 non-minimal couplings.

Confirmed conditions are satisfied in linearized massive gravity.

Abstract

Free massive higher spin fields in weak background gravitational fields are discussed. Contrary to the spin one case, higher spin fields should have nontrivial non-minimal couplings to the curvature. A precise analysis is given for the spin 2 case, and it is shown that two conditions should be satisfied among five non-minimal coupling constants, which we derive both in the Hamiltonian and Lagrangian formalisms. It is checked that the linearized limit of the massive gravity theory indeed has the non-minimal couplings that satisfy the conditions. We also discuss the form of the non-minimal couplings for the spin 3 case.