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Simplicity of polygon Wilson loops in \( \mathcal{N} \) = 4 SYM

  • Andreas Brandhuber
  • Paul Heslop
  • Valentin V. Khoze
  • Gabriele Travaglini
Article

Abstract

Wilson loops with lightlike polygonal contours have been conjectured to be equivalent to MHV scattering amplitudes in \( \mathcal{N} \) = 4 super Yang-Mills. We compute such Wilson loops for special polygonal contours at two loops in perturbation theory. Specifically, we concentrate on the remainder function \( \mathcal{R} \), obtained by subtracting the known ABDK/BDS ansatz from the Wilson loop. First, we consider a particular two dimensional eight-point kinematics studied at strong coupling by Alday and Maldacena. We find numerical evidence that \( \mathcal{R} \) is the same at weak and at strong coupling, up to an overall, coupling-dependent constant. This suggests a universality of the remainder function at strong and weak coupling for generic null polygonal Wilson loops, and therefore for arbitrary MHV amplitudes in \( \mathcal{N} \) = 4 super Yang-Mills. We analyse the consequences of this statement. We further consider regular n-gons, and find that the remainder function is linear in n at large n through numerical computations performed up to n = 30. This reproduces a general feature of the corresponding strong-coupling result.

Keywords

Supersymmetry and Duality Extended Supersymmetry Duality in Gauge Field Theories AdS-CFT Correspondence 

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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Andreas Brandhuber
    • 1
  • Paul Heslop
    • 2
  • Valentin V. Khoze
    • 3
  • Gabriele Travaglini
    • 1
  1. 1.Centre for Research in String Theory, Department of PhysicsQueen Mary University of LondonLondonUnited Kingdom
  2. 2.Institute for Particle Physics Phenomenology, Department of Mathematical Sciences and Department of PhysicsDurham UniversityDurhamUnited Kingdom
  3. 3.Institute for Particle Physics Phenomenology, Department of PhysicsDurham UniversityDurhamUnited Kingdom

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