Abstract
We show that scattering amplitudes in planar 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.
Highlights
Over the last years there has been tremendous progress in understanding the structure of the S-matrix of the N = 4 Super Yang-Mills (SYM) theory
We show that scattering amplitudes in planar 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 be computed using Stokes’ theorem. We apply this framework to maximally helicity violating (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
Summary
The aim of this paper is to study a kinematic limit, the multi-Regge limit, where we can completely describe the geometry underlying the scattering for any number external particles, and we can completely classify all the iterated integrals that appear in the final result The study of this limit has its origins not in N = 4 SYM, but it has been known since the early days of QCD that in the Regge limit s |t| scattering amplitudes exhibit a rich analytic structure. We present a complete classification of leading singularities in MRK to LLA and obtain explicit results for all non-MHV amplitudes up to four loops and with up eight external legs. All the results obtained in this paper are provided in computer-readable form as ancillary material with the arXiv submission of this paper
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