Abstract
The Einstein action with vanishing cosmological constant is for appropriate field content the unique local action which is regular at the fixed point of affine coordinate transformations. Imposing this regularity requirement one excludes also Wess-Zumino counterterms which trade gravitational anomalies for Lorentz anomalies. One has to expect dilatational and SL ( D) anomalies. If these anomalies are absent and if the regularity of the quantum vertex functional can be controlled then Einstein gravity is renormalizable.
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