Recent experiments have found an universal value for the dynamic conductivity in graphene, fully confirming theoretical predictions based on a non interacting tight binding model. This however poses a problem since one could expect a many body renormalization of the non interacting value of the conductivity due to the interaction. In the case of fermions on the honeycomb lattice with Hubbard interactions we have proved a theorem, related to the Adler-Bardeen non renormalization of the anomalies, ensuring that all the interaction corrections to the conductivity are exactly vanishing, even if the wave function renormalization and the Fermi velocity acquire finite renormalizations. In the case of interaction with the e.m. field, the wave function renormalization is infinite but again, at least at lowest order in the renormalized
expansion, the interaction corrections to the conductivity are vanishing. Extensions to bilayer graphene will be also discussed.
