Inconsistency of interacting, multi-graviton theories

By Nicolas Boulanger, T. Damour, L. Gualtieri, M. Henneaux. 2000

222 citations recorded by the source corpus.

We investigate, in any space-time dimension ≥3, the problem of consistent couplings for a (finite or infinite) 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 (or integral) 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. © 2001 Elsevier Science B.V.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4e5851bc2a48ac285403f781ef14f88581ddcf61

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Citations in the corpus

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Interacting spin-2 fields (2012, background): “(This does not contradict theorems forbidding multiple interacting massless gravitons [20], since the islands don’t interact with each other.”
How higher-spin gravity surpasses the spin-two barrier (2010, background): “ted out in [24, 25] to which we refer for related discussions. Let us note that the existence of colored gravitons in extended higher-spin theories does not enter in contradiction with the results of [49], since there it was assumed that the ﬁelds considered could have spin 2 at most and the backgro”
f(R) Theories (2010, background): “For example, besides the graviton, another spin-2 particle typically appears, which however, has a kinetic term opposite in sign with respect to the standard one [572, 67, 302, 465, 153, 303, 99].”
Theoretical Aspects of Massive Gravity (2011, background): “models and dimensional de-construction [108,109]. When multiple gravitons are present, all but one must become massive, since there are no non-trivial interactions between multiple massless gravitons [110], and these gravitons mimic the Kaluza-Klein spectrum of a discrete extra dimension. Other work”
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On the uniqueness of higher-spin symmetries in AdS and CFT (2013, background): “placed with (1.10) and the gauge transformations are properly deformed. 3 Jacobi identity In this section we recall some basic facts about consistent deformations of a free gauge theory, and refer to [31,43,44] for more details. In particular, we want to recall that the associativity of the inﬁnites”
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