The method of uniqueness and the optical conductivity of graphene: new application of a powerful technique for multi-loop calculations

We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation of a two-loop massless propagator Feynman diagram with a non-integer index on the central line. The result is applied to the computation of the optical conductivity of graphene at the infra-red Lorentz invariant fixed point. The effect of counter-terms is analysed. A brief comparison with the non-relativistic case is included.
Comment: Prepared for the Vth International Conference "Models in Quantum Field Theory" dedicated to Prof. Aleksandr Nikolaevich Vasiliev. LaTeX file with feynMF package. 15 pages, 4 figures (v2) Minor modifications (some per referee's comments)