MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops

Abstract

It is a remarkable fact that MHV amplitudes in maximally supersymmetric Yang-Mills theory at arbitrary loop order can be written as the product of the tree amplitude with the same helicity configuration and a universal, helicity-blind function of the kinematic invariants. In this note we show how for one-loop MHV amplitudes with an arbitrary number of external legs this universal function can be derived using Wilson loops. Our result is in precise agreement with the known expression for the infinite sequence of MHV amplitudes in N=4 super Yang-Mills. In the four-point case, we are able to reproduce the expression of the amplitude to all orders in the dimensional regularisation parameter epsilon. This prescription disentangles cleanly infrared divergences and finite terms, and leads to an intriguing one-to-one mapping between certain Wilson loop diagrams and (finite) two-mass easy box functions.

17 pages, 3 figures. v2: minor clarifications and references added

References in corpus (4)

• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• One-loop MHV Rules and Pure Yang-Mills
• Infrared Limit of Gluon Amplitudes at Strong Coupling
• Scattering amplitudes in strongly coupled N=4 SYM from semiclassical strings in AdS

Cited by in corpus (17)

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• Generating AdS String Solutions
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• New Dual Conformally Invariant Off-Shell Integrals
• Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface
• Some properties of the Alday-Maldacena minimum
• Gluon scattering in $\mathcal{N}=4$ Super Yang-Mills at finite temperature
• Lectures on Scattering Amplitudes via AdS/CFT
• Boundary Ring or a Way to Construct Approximate NG Solutions with Polygon Boundary Conditions. II. Polygons which admit an inscribed circle
• Gluon Scattering in Deformed N=4 SYM
• Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
• "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle
• Matching gluon scattering amplitudes and Wilson loops in off-shell regularization