Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills

Details Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills

2011-12-05

arxiv.org/abs/1112.1060v1

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, 3 figures

Scientific paper

We derive a set of first-order differential equations obeyed by the S-matrix of planar maximally supersymmetric Yang-Mills theory. The equations, based on the Yangian symmetry of the theory, involve only finite and regulator-independent quantities and uniquely determine the all-loop S-matrix. When expanded in powers of the coupling they give derivatives of amplitudes as single integrals over lower-loop, higher-point amplitudes/Wilson loops. We outline a derivation for the equations using the Operator Product Expansion for Wilson loops. We apply them on a few examples at two- and three-loops, reproducing a recent result on the two-loop NMHV hexagon and fixing previously undermined coefficients in a recent Ansatz for the three-loop MHV hexagon. In addition, we consider amplitudes restricted to a two-dimensional subspace of Minkowski space and derive a particularly simple closed set of equations in that case.

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