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Infinities in Quantum Gravities

We first present a review, intended for classical relativists, of the ultraviolet difficulties faced by local quantum gravity theories in both the usual Einstein versions and in their supergravity extensions, at least perturbatively. These problems, present in arbitrary dimensions, are traceable to the dimensionality of the Einstein constant.We then summarize very recent results about supergravity at the highest allowed dimension, D = 11, showing that also this unique model suffers from infinities already at 2 loops, despite its high degree of supersymmetry. The conclusion is that there is no viable nonghost quantum field model that includes general relativity.