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We calculate the optical (cutoff >> frequency >> temperature) conductivity inclean graphene in the ultimate low-energy regime, when retardation effects ofthe electromagnetic interaction become important and when the full Lorentzsymmetry emerges. In contrast to what happens with the short range or with theCoulomb long-range instantaneous interactions, the optical conductivity is nowno longer equal to its non interacting value, but acquires universalcorrections in powers of the fine structure constant. The coefficient of thefirst order correction is computed, and found to be of order one. We alsopresent the result for the conductivity in the large-N limit, with $N$ as thenumber of Dirac fermions species, to the order $1/N^2$.

Universal conductivity of graphene in the ultra-relativistic regime