Tree-level amplitudes and dual superconformal symmetry

TL;DR

This paper reviews the structure of tree-level gauge theory scattering amplitudes, highlighting a compact expression in N=4 supersymmetric theory that exhibits dual superconformal symmetry and extends to loop integrands and higher dimensions.

Contribution

It presents a unified, compact formulation of tree-level amplitudes in N=4 SYM and discusses the extension of dual superconformal symmetry to loops and higher-dimensional theories.

Findings

Compact expression for all tree-level amplitudes in N=4 SYM

Identification of dual superconformal symmetry in amplitudes

Extension of dual conformal symmetry to loop integrands and higher dimensions

Abstract

We review the structure of gauge theory scattering amplitudes at tree level and describe how a compact expression can be found which encodes all the tree-level amplitudes in the maximally supersymmetric N=4 theory. The expressions for the amplitudes reveal a dual superconformal symmetry. We describe how these ideas can be extended to leading singularities and the loop integrand in the planar theory and discuss the appearance of dual conformal symmetry in higher-dimensional gauge theories. This article is an invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories".