Renormalization Group for Dirac Metals

There is a wide class of quantum many body systems whose elementary excitations are well described in terms of massless Dirac particles; the most celebrated example is Graphene, but other examples include Spin Chains or Weyl semimetals. The methods developed in the last years in Constructive Quantum Field Theory and based on Renormalization Group are quite suitable to study such systems, and can provide mathematically rigorous results. In particular I will describe recent universality results obtained for the conductivity written in terms of Kubo formula, which in certain cases solved some controversy present in the physical literature.