One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills

TL;DR

This paper investigates how superconformal and Yangian symmetries of scattering amplitudes in N=4 Super Yang-Mills theory are affected at one-loop order, identifying anomalies and proposing deformations to restore these symmetries.

Contribution

It introduces a universal one-loop deformation of symmetry generators that cancels anomalies, based on tree-level data, extending symmetry understanding beyond tree level.

Findings

Computed one-loop superconformal anomalies using unitarity cuts.

Proposed a universal deformation of symmetry generators to cancel anomalies.

Validated the deformation with explicit checks on MHV and 6-point NMHV amplitudes.

Abstract

Recently it has been argued that tree-level scattering amplitudes in N=4 Yang-Mills theory are uniquely determined by a careful study of their superconformal and Yangian symmetries. However, at one-loop order these symmetries are known to become anomalous due to infrared divergences. We compute these one-loop anomalies for amplitudes defined through dimensional regularisation by studying the tree-level symmetry transformations of the unitarity branch cuts, keeping track of the crucial collinear terms arising from the holomorphic anomaly. We extract the superconformal anomalies and show that they may be cancelled through a universal one-loop deformation of the tree-level symmetry generators which involves only tree-level data. Specialising to the planar theory we also obtain the analogous deformation for the level-one Yangian generator of momentum. Explicit checks of our one-loop deformation are performed for MHV and the 6-point NMHV amplitudes.