Multi-graviton theories : yes-go and no-go results

TL;DR

This paper explores the possibilities and limitations of constructing consistent theories involving multiple massless spin-two fields, identifying conditions under which such interactions are possible or forbidden.

Contribution

It provides comprehensive yes-go and no-go results on cross-couplings of multiple gravitons and introduces multi-Weyl-graviton theories with unbounded energy.

Findings

Certain multi-graviton interactions are consistent with deformation theory.

Multi-Weyl-graviton theories exist but lack energy boundedness.

No-go results restrict some types of cross-interactions.

Abstract

We report yes-go and no-go results on consistent cross-couplings for a collection of gravitons. Motivated by the search of theories where multiplets of massless spin-two fields cross-interact, we look for all the consistent deformations of a positive sum of Pauli-Fierz actions. We also investigate the problem of deforming a (positive and negative) sum of linearized Weyl gravity actions and show explicitly that there exists multi-Weyl-graviton theories. As the single-graviton Weyl theory, these theories do not have an energy bounded from below.