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The long standing controversy concerning the effect of electron - electroninteraction on the electrical conductivity of an ideal graphene sheet issettled. Performing the calculation directly in the tight binding approachwithout the usual prior reduction to the massless Dirac (Weyl) theory, it isfound that, to leading order in the interaction strength alpha =e^2/(hbar*v0),the DC conductivity sigma/sigma0=1+C*alpha is significantly enhanced withrespect to the independent-electrons result sigma0, i.e. with the value C =0.26. The ambiguity characterizing the various existing approaches isnontrivial and related to the chiral anomaly in the system. In order toseparate the energy scales in a model with massless fermions, contributionsfrom regions of the Brillouin zone away from the Dirac points have to beaccounted for. Experimental consequences of the relatively strong interactioneffect are briefly discussed.

Chiral anomaly and strength of the electron-electron interaction in graphene