Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry

TL;DR

This paper reviews the dual superconformal symmetry in planar N=4 super Yang-Mills theory, highlighting its role in constraining scattering amplitudes, its connection to Wilson loops, and its relation to integrability via Yangian algebra.

Contribution

It provides a comprehensive overview of dual superconformal symmetry, including dual formulations and classification of invariants, advancing understanding of integrability in the theory.

Findings

Dual superconformal symmetry constrains scattering amplitudes.

Connection between amplitudes and Wilson loops on light-like polygons.

Yangian algebra emerges from combined superconformal and dual superconformal symmetries.

Abstract

Scattering amplitudes in planar N=4 super Yang-Mills theory reveal a remarkable symmetry structure. In addition to the superconformal symmetry of the Lagrangian of the theory, the planar amplitudes exhibit a dual superconformal symmetry. The presence of this additional symmetry imposes strong restrictions on the amplitudes and is connected to a duality relating scattering amplitudes to Wilson loops defined on polygonal light-like contours. The combination of the superconformal and dual superconformal symmetries gives rise to a Yangian, an algebraic structure which is known to be related to the appearance of integrability in other regimes of the theory. We discuss two dual formulations of the symmetry and address the classification of its invariants.