Absence of interaction corrections in the optical conductivity of graphene

The exact vanishing of the interaction corrections to the zero temperature optical conductivity of undoped graphene in the presence of weak short-range interactions is rigorously established. Our results are in agreement with measurements of graphene's ac conductivity in a range of frequencies between the temperature and the bandwidth. Even if irrelevant in the renormalization group sense, lattice effects and nonlinear bands are essential for the universality of the conductivity.