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

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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.

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Authors and Affiliations

  1. Centre for Research in String Theory, Department of Physics, Queen Mary University of London, Mile End Road, London, E1 4NS, United Kingdom

    Andreas Brandhuber & Gabriele Travaglini

  2. Institute for Particle Physics Phenomenology, Department of Mathematical Sciences and Department of Physics, Durham University, Durham, DH1 3LE, United Kingdom

    Paul Heslop

  3. Institute for Particle Physics Phenomenology, Department of Physics, Durham University, Durham, DH1 3LE, United Kingdom

    Valentin V. Khoze

Authors
  1. Andreas Brandhuber
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  2. Paul Heslop
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  3. Valentin V. Khoze
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  4. Gabriele Travaglini
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Correspondence to Andreas Brandhuber.

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ArXiv ePrint: 0910.4898

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Brandhuber, A., Heslop, P., Khoze, V.V. et al. Simplicity of polygon Wilson loops in \( \mathcal{N} \) = 4 SYM. J. High Energ. Phys. 2010, 50 (2010). https://doi.org/10.1007/JHEP01(2010)050

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