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Galaxy Rotation Curves from General Relativity with Infrared Renormalization Group Effects

We review our contribution to infrared Renormalization Group (RG) effects to General Relativity in the context of galaxies. Considering the effective action approach to Quantum Field Theory in curved background, we argued that the proper RG energy scale, in the weak field limit, should be related to the Newtonian potential. In the galaxy context, even without dark matter, this led to a remarkably small gravitational coupling G variation (about or less than 10^{-12} of its value per light-year), while also capable of generating galaxy rotation curves about as good as the best phenomenological dark matter profiles (considering both the rotation curve shape and the expected mass-to-light ratios). Here we also comment on related developments, open issues and perspectives.