Title: Musings and some results about non-perturbative RG

Abstract:
I will motivate why non-perturbative RG is an unfinished business, and what kind of developments are needed in this area. I will then describe recent rigorous work about RG fixed points in a model of symplectic fermions with a long-range kinetic term and a local quartic interaction. This may be the simplest field theory in which a non-gaussian fixed point can be shown to exist without any truncation or approximation. It is a perfect toy model where various folklore properties of RG fixed points (universality of critical exponents, conformal invariance, etc) could be examined explicitly. It also offers some hints for better numerical implementations of non-perturbative RG. Based on 2008.04361 with Alessandro Giuliani and Vieri Mastropietro.

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