Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2014-16

Livia Ferro, Tomasz Lukowski, Matthias Staudacher


N=4 Scattering Amplitudes and the Deformed Graßmannian


Abstract: Some time ago the general tree-level scattering amplitudes of N = 4 Super Yang-Mills theory were expressed as certain Gramannian 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 modication of the measure of the Gramannian 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.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2014-16


15 pp.