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

  • Vittorio Del Duca
  • Stefan Druc
  • James Drummond
  • Claude Duhr
  • Falko Dulat
  • Robin Marzucca
  • Georgios Papathanasiou
  • Bram Verbeek
Open Access
Article

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.

Keywords

Supersymmetric gauge theory Gauge Symmetry Extended Supersymmetry 

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Vittorio Del Duca
    • 1
  • Stefan Druc
    • 2
  • James Drummond
    • 2
  • Claude Duhr
    • 3
    • 4
  • Falko Dulat
    • 5
  • Robin Marzucca
    • 4
  • Georgios Papathanasiou
    • 5
  • Bram Verbeek
    • 4
  1. 1.Institute for Theoretical Physics, ETH ZürichZürichSwitzerland
  2. 2.School of Physics & AstronomyUniversity of SouthamptonSouthamptonUK
  3. 3.Theoretical Physics Department, CERNGeneva 23Switzerland
  4. 4.Center for Cosmology, Particle Physics and Phenomenology (CP3)Université catholique de LouvainLouvain-La-NeuveBelgium
  5. 5.SLAC National Accelerator LaboratoryStanford UniversityStanfordUSA

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