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Interaction corrections to the minimal conductivity of graphene via dimensional regularization

We compute the two-loop interaction correction to the minimal conductivity of disorder-free intrinsic graphene with the help of dimensional regularization. The calculation is done in two different ways: via density-density and via current-current correlation functions. Upon properly renormalizing the perturbation theory, in both cases, we find that: $σ= σ_0\,( 1 + \al\,(19-6π)/12) \approx σ_0 \,(1 + 0.01\, \al)$, where $\al = e^2 / (4 π\hbar v)$ is the renormalized fine structure constant and $σ_0 = e^2 / (4 \hbar)$. Our results are consistent with experimental uncertainties and resolve a theoretical dispute.