2009/04/02 by A. Gorsky, A Gorsky, A. Zhiboedov +1 · 9 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Amplitude #Black Holes and Theoretical Physics #Duality (order theory) #Feynman diagram #Generalization #Noncommutative and Quantum Gravity Theories #Polygon (computer graphics) #T-duality #Vertex (graph theory) #hep-th
paper · pdf · doi:10.1088/1751-8113/42/35/355214
published in Journal of Physics A Mathematical and Theoretical 42(35), 355214 (Institute of Physics) · 29 pages
arxiv created 2009/04/02 · openalex publication_date 2009/08/17 · arxiv updated 2010/12/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.