Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization

TL;DR

This paper introduces a spectral parameter deformation of scattering amplitudes in N=4 super Yang-Mills, linking them to integrable R-matrices and proposing a new symmetry-preserving regularization method.

Contribution

It establishes a novel connection between spectral parameter deformations and scattering amplitudes, providing new integrable structures and a potential regularization scheme.

Findings

Deformed four-point functions relate to one-loop R-matrices.

Three-point functions produce new R-matrices satisfying bootstrap equations.

Spectral parameter may serve as a symmetry-respecting regulator.

Abstract

Planar N=4 super Yang-Mills appears to be integrable. While this allows to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R-matrix of the integrable N=4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R-matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of non-integrable four-dimensional field theories.