Interactions of multiple spin-2 fields beyond pairwise couplings

TL;DR

This paper introduces a new class of ghost-free multi-spin-2 field theories with genuine multi-field interactions beyond pairwise couplings, expanding the landscape of consistent higher-spin interactions.

Contribution

It presents a novel construction of multi-spin-2 interactions involving integrating out nondynamical fields, which are not reducible to metric-based interactions, demonstrating ghost-free stability.

Findings

Established ghost-free multi-spin-2 interactions beyond pairwise couplings

Derived multi-vierbein interactions not always expressible via metrics

Confirmed absence of ghost instabilities in the new theories

Abstract

Thus far, all known ghost-free interactions of multiple spin-2 fields have involved at most pairwise couplings of the fields, which are direct generalizations of bimetric interactions. Here we present a class of spin-2 theories with genuine multi-field interactions, and explicitly demonstrate the absence of ghost instabilities. The construction involves integrating out a nondynamical field in a theory of spin-2 fields with only pairwise ghost-free interactions. The new multi-vierbein interactions generated are not always expressible in terms of the associated metrics.