Spin-1 massless particles are transverse waves, so they need at least three space-time dimensions to exists. As for gravitons, I think they are still not possible in three dimensions, and to reveal their true nature one needs at least four dimensions; otherwise there would be no way to distinguish a graviton form a vector in such a three dimensional universe. Other argument against it is the fact that there's only (grav.) radiation in four or more dimensions, but I'm looking for a "theorem" more in the context of field theory.
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