The conductivity of pure graphene

Pure graphene, in the absence of impurities or bias voltage, is described by a theory of Dirac fermions with Coulomb interactions. We argue that this theory has a finite conductivity, $\sigma$, and show that at frequencies $\omega \ll k_B T/\hbar$ (where $T$ is absolute temperature) $\sigma = \Xi (e^2/h) (\ln (W/T))^2 $, where $W$ is the bandwidth, and $\Xi$ is a {\em universal} number. We compute $\Xi$ by the solution of a quantum Boltzmann equation. The influence of a dilute concentration of impurities and finite bias voltage is also discussed.