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

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.

arXiv comment19 pages; discussion on spin 3 added, references added (v2); footnote 9 corrected (v3)

References in corpus (11)

• Generalization of the Fierz-Pauli Action
• Theoretical Aspects of Massive Gravity
• Bimetric Gravity from Ghost-free Massive Gravity
• On Non-Linear Actions for Massive Gravity
• Derivative self-interactions for a massive vector field
• Geometric Lagrangians for massive higher-spin fields
• On the relation between local and geometric Lagrangians for higher spins
• Linear spin-2 fields in most general backgrounds
• On interactions of higher spin fields with gravity and branes in AdS_5
• A No-Go Theorem for the Consistent Quantization of Spin 3/2 Fields on General Curved Spacetimes
• Massive graviton on arbitrary background: derivation, syzygies, applications