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Notes on the scattering amplitude – Wilson loop duality. (English) Zbl 1298.81357
Summary: We consider the duality between the four-dimensional S-matrix of planar maximally supersymmetric Yang-Mills theory and the expectation value of polygonal shaped Wilson loops in the same theory. We extend the duality to amplitudes with arbitrary helicity states by introducing a suitable supersymmetric extension of the Wilson loop. We show that this object is determined by a host of recursion relations, which are valid at tree level and at loop level for a certain “loop integrand” defined within the Lagrangian insertion procedure. These recursion relations reproduce the BCFW ones obeyed by tree-level scattering amplitudes, as well as their extension to loop integrands which appeared recently in the literature, establishing the duality to all orders in perturbation theory. Finally, we propose that a certain set of finite correlation functions can be used to compute all first derivatives of the logarithm of MHV amplitudes.

MSC:
81U20 \(S\)-matrix theory, etc. in quantum theory
81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces
81T18 Feynman diagrams
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