Timothy Goddard, Paul Heslop, Valentin V. Khoze
We consider scattering amplitudes in planar N=4 supersymmetric Yang-Mills theory in special kinematics where all external four-dimensional momenta are restricted to a (1+1)-dimensional subspace. Using factorisation properties of the superamplitude under multi-collinear limits and other symmetries of the problem, we show how expressions for general n-point amplitudes for any number of loops l>0 are assembled from a finite number of amplitudes with low values for n. These more elementary building blocks are expressions for 8-point amplitudes, S_8, plus some higher-point functions, S_m, with m divisible by four, and m less than or equal to 4l for MHV amplitudes, and which are constrained to vanish in all appropriate collinear limits. This procedure results in a surprisingly compact expression for an n-point amplitude and provides a universal uplift of lower-point amplitudes to all higher-point amplitudes. It works at any loop-level l>0 and for any MHV or N^kMHV amplitude. We compare this with explicit examples involving n-point MHV amplitudes at 2-loops and 10-point MHV amplitudes at 3-loops. Tree-level superamplitudes have different properties and are treated separately from loop-level amplitudes in our approach. To illustrate this we derive an expression for n-point tree-level NMHV amplitudes in special kinematics.
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http://arxiv.org/abs/1205.3448
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