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Inconsistency of interacting, multi-graviton theories

Nicolas Boulanger·Thibault Damour·Leonardo Gualtieri·Marc Henneaux
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Abstract

We investigate, in any spacetime dimension >=3, the problem of consistent couplings for a finite collection of massless, spin-2 fields described, in the free limit, by a sum of Pauli-Fierz actions. We show that there is no consistent (ghost-free) coupling, with at most two derivatives of the fields, that can mix the various "gravitons". In other words, there are no Yang-Mills-like spin-2 theories. The only possible deformations are given by a sum of individual Einstein-Hilbert actions. The impossibility of cross-couplings subsists in the presence of scalar matter. Our approach is based on the BRST-based deformation point of view and uses results on the so-called "characteristic cohomology" for massless spin-2 fields which are explained in detail.

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Nicolas Boulanger, Thibault Damour, Leonardo Gualtieri, Marc Henneaux. 2000-10-05. Inconsistency of interacting, multi-graviton theories. https://doi.org/10.1016/s0550-3213(00)00718-5

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