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High Energy Physics - Theory, hep-th
Abstract:
Some time ago the general tree-level scattering amplitudes of N=4 Super
Yang-Mills theory were expressed as certain Grassmannian contour integrals.
These remarkable formulas allow to clearly expose the super-conformal, dual
super-conformal, and Yangian symmetries of the amplitudes. Using ideas from
integrability it was recently shown that the building blocks of the amplitudes
permit a natural multi-parameter deformation. However, this approach had been
criticized by the observation that it seemed impossible to reassemble the
building blocks into Yangian-invariant deformed non-MHV amplitudes. In this
note we demonstrate that the deformations may be succinctly summarized by a
simple modification of the measure of the Grassmannian integrals, leading to a
Yangian-invariant deformation of the general tree-level amplitudes.
Interestingly, the deformed building-blocks appear as residues of poles in the
spectral parameter planes. Given that the contour integrals also contain
information on the amplitudes at loop-level, we expect the deformations to be
useful there as well. In particular, applying meromorphicity arguments, they
may be expected to regulate all notorious infrared divergences. We also point
out relations to Gelfand hypergeometric functions and the quantum
Knizhnik-Zamolodchikov equations.
