emerging description is in terms of [*disordered Dirac fermions*]{}, which were extensively analyzed along the years. In the case of [*chiral preserving disorder*]{} it was found that the density of states is vanishing with a critical exponent (non trivial function of the disorder strength) but the conductivity is [*universal*]{} and not depending from the disorder amplitude, see [@LFSG; @NTW]. Such results, obtained using the replica trick, were confirmed and extended by a Supersymmetric analysis of such models [@ASZ; @Mu1; @Mu2] leading to a functional integral in Bosonic and Grassmann variables and a [*local*]{} quartic interaction. It is rather natural to relate such results to the universal conductivity found by transport measurements in graphene [@Mi], despite the understanding of why the dominant disorder in graphene should preserve chirality is an open issue which may be related to how the sample is produced. However, even assuming that disorder preserves chirality, several questions still remain to be understood. The results in [@LFSG; @NTW; @ASZ; @Mu1; @Mu2] on Dirac fermions with disorder where found assuming [*delta correlated*]{} disorder and an unbounded fermionic dispersion relation (no ultraviolet cut-offs). Such features makes an exact analysis possible (even non perturbative, see [@Mu2] and references therein) but produce 