Interacting Spin-2 Fields

TL;DR

This paper develops a vielbein-based framework for consistent interactions of multiple spin-2 fields in any dimension, ensuring ghost-free theories and establishing equivalence with known massive gravity models.

Contribution

It introduces a vielbein formulation for multi-spin-2 interactions, proving ghost-freedom to all orders and relating it to existing massive gravity theories.

Findings

Theories have the necessary constraints to eliminate ghosts.

Vielbein formulation simplifies ghost-freedom proofs.

Equivalence established between vielbein and known massive gravity models.

Abstract

We construct consistent theories of multiple interacting spin-2 fields in arbitrary spacetime dimensions using a vielbein formulation. We show that these theories have the additional primary constraints needed to eliminate potential ghosts, to all orders in the fields, and to all orders beyond any decoupling limit. We postulate that the number of spin-2 fields interacting at a single vertex is limited by the number of spacetime dimensions. We then show that, for the case of two spin-2 fields, the vielbein theory is equivalent to the recently proposed theories of ghost-free massive gravity and bi-metric gravity. The vielbein formulation greatly simplifies the proof that these theories have an extra primary constraint which eliminates the Boulware-Deser ghost.