The Imaginary Part of the N = 4 Super-Yang-Mills Two-Loop Six-Point MHV Amplitude in Multi-Regge Kinematics

Abstract

The precise form of the multi-Regge asymptotics of the two-loop six-point MHV amplitude in N = 4 Super-Yang-Mills theory has been a subject of recent controversy. In this paper we utilize the amplitude/Wilson loop correspondence to obtain precise numerical results for the imaginary part of these asymptotics. The region of phase-space that we consider is interesting because it allowed Bartels, Lipatov, and Sabio Vera to determine that the two-loop six-point MHV amplitude is not fixed by the BDS ansatz. They proceeded by working in the framework of a high energy effective action, thus side-stepping the need for an arduous two-loop calculation. Our numerical results are consistent with the predictions of Bartels, Lipatov, and Sabio Vera for the leading-log asymptotics.

18 pages, 2 figures. In version 2 some remarks made about 0809.1632 v3 were excised since it was brought to our attention that the preprint 0809.1632 v3 is actually not the final version of that article

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• Gluon scattering amplitudes at strong coupling
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• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
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• Iterative Structure Within The Five-Particle Two-Loop Amplitude
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• Iterated amplitudes in the high-energy limit

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• Classical Polylogarithms for Amplitudes and Wilson Loops
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Hexagon functions and the three-loop remainder function
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Single-valued harmonic polylogarithms and the multi-Regge limit
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• Mandelstam cuts and light-like Wilson loops in N=4 SUSY
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• Simplicity of Polygon Wilson Loops in N=4 SYM
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• Wilson loop OPE, analytic continuation and multi-Regge limit
• The six-point remainder function to all loop orders in the multi-Regge limit
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Integrable spin chains and scattering amplitudes
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops