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High Energy Physics - Theory, hep-th
Abstract:
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.
