range of frequencies and very close to the [*universal*]{} value $(\pi/2)(e^2/h)$, which also happens to be the value found for the system of non-interacting $2d$ Dirac fermions [@LFSG], a remarkable result in view of the fact that interactions are not particularly weak. In transport measurements an [*universal*]{} value for the conductivity is also found, of order of the conductivity quantum $e^2/h$ [@N3]; again a surprising result in view of the presence of disorder which is surely relevant in such experiments.

It is of course important to understand if and under which conditions such universality can be understood theoretically. In presence of weak short range interactions, after first perturbative computations claiming non vanishing corrections, it was finally rigorously proved [@GMP] that the optical conductivity is [*exactly equal*]{} to its non interacting value. Note that the emerging description is in terms of a Nambu-Jona Lasinio model and the natural cut-off provided by honeycomb lattice ensures the correct symmetries and allows the proof of the complete cancellation of the interaction corrections. On the other hand, in the case of [*long range*]{} Coulomb interaction it has been predicted that the optical conductivity is still equal to the non interacting value [@H0], the argument this 