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

TL;DR

This paper reviews the method of uniqueness for multi-loop calculations in conformal theories, demonstrating its application to compute graphene's optical conductivity at a fixed point, including counter-term effects and comparisons with non-relativistic cases.

Contribution

It introduces a new application of the method of uniqueness to evaluate the optical conductivity of graphene at a conformal fixed point.

Findings

Successful evaluation of a two-loop Feynman diagram using the method of uniqueness.

Application of the technique to compute graphene's optical conductivity.

Analysis of counter-term effects and comparison with non-relativistic cases.

Abstract

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.