Exact Superconformal and Yangian Symmetry of Scattering Amplitudes

TL;DR

This paper reviews recent advances in understanding the exact superconformal and Yangian symmetries of scattering amplitudes in N=4 super Yang-Mills theory, including how to correct for anomalies at tree and loop levels.

Contribution

It explains how to restore superconformal symmetry in scattering amplitudes by correcting their representations and discusses the inheritance of these corrections by Yangian symmetry.

Findings

Superconformal symmetry can be restored at tree and loop levels.

Yangian symmetry inherits corrections from superconformal symmetry.

Relations between invariants and Grassmannian generating functions are explored.

Abstract

We review recent progress in the understanding of symmetries for scattering amplitudes in N=4 superconformal Yang-Mills theory. It is summarized how the superficial breaking of superconformal symmetry by collinear anomalies and the renormalization process can be cured at tree and loop level. This is achieved by correcting the representation of the superconformal group on amplitudes. Moreover, we comment on the Yangian symmetry of scattering amplitudes and how it inherits these correction terms from the ordinary Lie algebra symmetry. Invariants under this algebra and their relation to the Grassmannian generating function for scattering amplitudes are discussed. Finally, parallel developments in N=6 superconformal Chern-Simons theory are summarized. This article is an invited review for a special issue of Journal of Physics A devoted to Scattering Amplitudes in Gauge Theories.