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Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
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  • Published: 25 August 2016

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

  • Vittorio Del Duca1,
  • Stefan Druc2,
  • James Drummond2,
  • Claude Duhr3,4,
  • Falko Dulat5,
  • Robin Marzucca4,
  • Georgios Papathanasiou5 &
  • …
  • Bram Verbeek4 

Journal of High Energy Physics volume 2016, Article number: 152 (2016) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

We show that scattering amplitudes in planar \( \mathcal{N}=4 \) Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

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Authors and Affiliations

  1. Institute for Theoretical Physics, ETH Zürich, Hönggerberg, 8093, Zürich, Switzerland

    Vittorio Del Duca

  2. School of Physics & Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ, UK

    Stefan Druc & James Drummond

  3. Theoretical Physics Department, CERN, Route de Meyrin, CH-1211, Geneva 23, Switzerland

    Claude Duhr

  4. Center for Cosmology, Particle Physics and Phenomenology (CP3), Université catholique de Louvain, Chemin du Cyclotron 2, 1348, Louvain-La-Neuve, Belgium

    Claude Duhr, Robin Marzucca & Bram Verbeek

  5. SLAC National Accelerator Laboratory, Stanford University, Stanford, CA, 94309, USA

    Falko Dulat & Georgios Papathanasiou

Authors
  1. Vittorio Del Duca
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  2. Stefan Druc
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  3. James Drummond
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  4. Claude Duhr
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  5. Falko Dulat
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  6. Robin Marzucca
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  7. Georgios Papathanasiou
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  8. Bram Verbeek
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Corresponding author

Correspondence to Claude Duhr.

Additional information

ArXiv ePrint: 1606.08807

On leave from Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, Italy. (Vittorio Del Duca)

On leave from the "Fonds National de la Recherche Scientifique" (FNRS), Belgium. (Claude Duhr)

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Del Duca, V., Druc, S., Drummond, J. et al. Multi-Regge kinematics and the moduli space of Riemann spheres with marked points. J. High Energ. Phys. 2016, 152 (2016). https://doi.org/10.1007/JHEP08(2016)152

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  • Received: 09 July 2016

  • Accepted: 05 August 2016

  • Published: 25 August 2016

  • DOI: https://doi.org/10.1007/JHEP08(2016)152

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Keywords

  • Supersymmetric gauge theory
  • Gauge Symmetry
  • Extended Supersymmetry
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