  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.

High Energy Physics - Theory