Wilson Loops in N=2 Superconformal Yang-Mills Theory

TL;DR

This paper performs a three-loop calculation comparing Wilson loops in N=4 and N=2 superconformal Yang-Mills theories, revealing a simplified diagrammatic structure and recovering known matrix model results.

Contribution

It introduces a streamlined diagrammatic approach for three-loop Wilson loop calculations in N=2 theories and connects these results to matrix model predictions.

Findings

Reduction in the number of Feynman diagrams needed

Recovery of the zeta(3) term from matrix model

Results applicable to loops of general shape

Abstract

We present a three-loop O(g^6) calculation of the difference between the expectation values of Wilson loops evaluated in N=4 and superconformal N=2 supersymmetric Yang-Mills theory with gauge group SU(N) using dimensional reduction. We find a massive reduction of required Feynman diagrams, leaving only certain two-matter-loop corrections to the gauge field and associated scalar propagator. This "diagrammatic difference" leaves a finite result proportional to the bare propagators and allows the recovery of the zeta(3) term coming from the matrix model for the 1/2 BPS circular Wilson loop in the N=2 theory. The result is valid also for closed Wilson loops of general shape. Comments are made concerning light-like polygons and supersymmetric loops in the plane and on S^2.