density of states is still anomalous but the conductivity has in general disorder-dependent corrections.

Therefore, the vanishing of the density of states with an anomalous exponent is a robust property for chiral disordered fermions, but the [*exact*]{} vanishing of the disorder corrections to the conductivity does not survive in general to the presence of a momentum cut-off. From a Renormalization Group point of view this is rather natural. In presence of chiral disorder the theory is [*marginal*]{} with a line of fixed points; therefore corrections are expected, as in the case of the optical conductivity in presence of e.m. interaction. From this perspective, it is the [*absence*]{} of corrections the more surprising feature of disordered Dirac fermions with no cut-off; as it will be clear from the subsequent analysis, it is a direct consequence of the validity of the Adler-Bardeen theorem and the exact cancellation of the chiral anomaly due to the supersymmetry, which is valid only when the momentum cut-off is removed. The presence of corrections to the conductivity in presence of an ultraviolet cut-off may have of course implications for the physics of graphene, in which a natural ultraviolet cut-off is provided by the honeycomb lattice.

The presence 