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Inconsistency of Interacting, Multi-Graviton Theories

机译：交互，多重力理论的不一致性

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The authors investigate, in any spacetime dimension > or = 3, the problem ofconsistent couplings for a finite collection of massless, spin-2 fields described, in the free limit, by a sum of Pauli-Fierz actions. The authors 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. The authors' 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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