No consistent cross-interactions for a collection of massless spin-2 fields

TL;DR

This paper proves a no-go theorem showing that multiple massless spin-2 fields cannot have consistent cross-interactions in dimensions greater than two, limiting possible couplings to separate Einstein-Hilbert actions.

Contribution

It establishes a rigorous no-go result for cross-couplings of multiple massless spin-2 fields using BRST deformation methods.

Findings

No consistent cross-interactions for multiple massless spin-2 fields in >2 dimensions.

Allowed deformations are sums of individual Einstein-Hilbert actions with cosmological terms.

Cross-couplings with more than two derivatives are excluded.

Abstract

We report a no-go theorem excluding consistent cross-couplings for a collection of massless, spin-2 fields described, in the free limit, by the sum of Pauli-Fierz actions (one for each field). We show that, in spacetime dimensions >2, there is no consistent coupling, with at most two derivatives of the fields, that can mix the various "gravitons". The only possible deformations are given by the sum of individual Einstein-Hilbert actions (one for each field) with cosmological terms. Our approach is based on the BRST-based deformation point of view.