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Wilson Loops in N=2 Superconformal Yang-Mills Theory

Roman Andree, Donovan Young

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.

Wilson Loops in N=2 Superconformal Yang-Mills Theory

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.

Paper Structure

This paper contains 10 sections, 41 equations, 4 figures.

Table of Contents

  1. Introduction and results
  2. Results from localization
  3. Perturbation theory
  4. One-loop corrected trivalent graph
  5. Comments on light-like loops and loops on $\mathbb{R}^2$ and $S^2$
  6. Zarembo loops in the plane
  7. Longitudes Wilson loop
  8. Light-like Wilson loops and scattering amplitudes
  9. Two-loop matter corrections
  10. The diagrams

Figures (4)

  • Figure 1: "Tree" type diagrams are identical in the two theories, and so their difference vanishes.
  • Figure 2: One-loop corrected tree-type diagrams are also identical in the two theories, and so their difference also vanishes.
  • Figure 3: After application of rules depicted in figures \ref{['fig:noloop']} and \ref{['fig:1loop']}, only the two-loop propagator, and 1-loop triple-vertex corrections remain at ${\cal O}(g^6)$.
  • Figure 4: One-matter-loop corrections to the triple vertex, shown (to reduce clutter) for the ${\cal N}=2$ theory only. In the ${\cal N}=4$ case internal lines are doubled.