One-loop derivation of the Wilson polygon - MHV amplitude duality

Abstract

We discuss the origin of the Wilson polygon - MHV amplitude duality at the perturbative level. It is shown that the duality for the MHV amplitudes at one-loop level can be proven upon the peculiar change of variables in Feynman parametrization and the use of the relation between Feynman integrals at the different space-time dimensions. Some generalization of the duality which implies the insertion of the particular vertex operator at the Wilson triangle is found for the 3-point function. We discuss analytical structure of Wilson loop diagrams and present the corresponding Landau equations. The geometrical interpretation of the loop diagram in terms of the hyperbolic geometry is discussed.

29 pages

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• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
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• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• Aspects of the N=4 SYM amplitude -- Wilson polygon duality
• Geometrical splitting and reduction of Feynman diagrams
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space