Conductivity of Coulomb interacting massless Dirac particles in graphene

The ac conductivity of the Coulomb interacting Dirac fermions in graphene is considered in the collisionless regime using a variant of the dimensional regularization with the spatial dimension $D=2-\epsilon$ for $\epsilon>0$. We show that this regularization procedure preserves the Ward-Takahashi identity associated with the charge conservation [1], and as such it can serve as a consistent regularization of the entire interacting field theory. As a consequence of the explicitly preserved $U(1)$ gauge symmetry, the dimensional regularization yields the same result for the Coulomb correction to the conductivity when calculated using the current-current and the density-density correlators, which is, nevertheless, different than the ones previously reported in the literature. References: [1] V. Juricic, O. Vafek, and I. F. Herbut, ArXiv:1009.3269 (Phys. Rev. B, in press).