Abstract: 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 presence of weak and short range interactions, a theorem valid for the Hubbard model on the honeycomb lattice ensures that all the interaction corrections to the conductivity are vanishing. The proof is based on a combination of Ward Identities and regularity properties obtained by convergent expansions. Some results for the case of long range interactions will be also presented.