N=4 Scattering Amplitudes and the Deformed Grassmannian

TL;DR

This paper introduces a simple measure modification in Grassmannian integrals that yields a Yangian-invariant deformation of tree-level N=4 Super Yang-Mills amplitudes, with potential applications to loop-level calculations and divergence regulation.

Contribution

It demonstrates a succinct measure deformation in Grassmannian integrals that preserves Yangian symmetry, addressing previous challenges in constructing deformed non-MHV amplitudes.

Findings

Deformed building blocks are residues of poles in spectral parameter planes.

The measure modification leads to a Yangian-invariant deformation of all tree-level amplitudes.

Potential to regulate infrared divergences at loop level using the deformation.

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.