Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory

TL;DR

This paper explores the role of spectral parameters in integrable models of N=4 Super Yang-Mills theory, proposing their inclusion in scattering amplitude calculations to preserve symmetry and control divergences.

Contribution

It introduces the spectral parameter into on-shell methods for scattering amplitudes, offering a new deformation that maintains Yangian symmetry under certain conditions.

Findings

Spectral parameter can be integrated into amplitude integrands.

Yangian symmetry can be preserved with the spectral deformation.

Potential for using the spectral parameter as an infrared regulator.

Abstract

Planar N=4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N=4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indeed be included into recent on-shell approaches to scattering amplitude integrands, providing a natural deformation of the latter. Under some constraints, Yangian symmetry is preserved. Finally we speculate that the spectral parameter might also be the regulator of choice for controlling the infrared divergences appearing when integrating the integrands in exactly four dimensions.