Renormalization Group flow and the Nash-Moser theorem

Abstract

The Renormalization Group (RG) Equation determines the flow of the effective action under changes in an artificial scale k, which roughly corresponds to the scale of the system under consideration. I report on a rigorous construction of a non-perturbative RG flow for the effective action in Lorentzian manifolds.  I sketch a proof of local existence of solutions for the RG equation, when a suitable Local Potential Approximation is considered. The proof is based on an application of the renown Nash-Moser theorem. Time permitting, I also discuss an application of the RG equation to quantum gravity.