Inconsistency of interacting, multi-graviton theories

We investigate, in any space-time dimension greater than or equal to 3, the problem of consistent couplings for a (finite or infinite) collection of m assless, spin-2 fields described, in the free limit, by a sum of Pauli-Fier z 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 po ssible deformations are given by a sum (or integral) of individual Einstein -Hilbert actions. The impossibility of cross-couplings subsists in the pres ence 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. (C) 2001 Elsevie r Science B.V. All rights reserved.