Bootstrapping six-gluon scattering in planar $\mathcal{N}=4$ super-Yang-Mills theory

Abstract

We describe the hexagon function bootstrap for solving for six-gluon scattering amplitudes in the large $N_c$ limit of $\mathcal{N}=4$ super-Yang-Mills theory. In this method, an ansatz for the finite part of these amplitudes is constrained at the level of amplitudes, not integrands, using boundary information. In the near-collinear limit, the dual picture of the amplitudes as Wilson loops leads to an operator product expansion which has been solved using integrability by Basso, Sever and Vieira. Factorization of the amplitudes in the multi-Regge limit provides additional boundary data. This bootstrap has been applied successfully through four loops for the maximally helicity violating (MHV) configuration of gluon helicities, and through three loops for the non-MHV case.

arXiv comment15 pages, 3 figures, 2 tables; contribution to the proceedings of Loops and Legs in Quantum Field Theory, 27 April - 2 May 2014, Weimar, Germany; v2, reference added

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Cited by in corpus (15)

• Bootstrapping an NMHV amplitude through three loops
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• OPE for all Helicity Amplitudes
• Rationalizing Loop Integration
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• A Note on Letters of Yangian Invariants
• The Wilson-loop $d\log$ representation for Feynman integrals
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• The four-loop six-gluon NMHV ratio function
• Anatomy of the Amplituhedron
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• The Multi-Regge Limit from the Wilson Loop OPE
• Cluster Functions and Scattering Amplitudes for Six and Seven Points