Hidden Simplicity of Gauge Theory Amplitudes

TL;DR

This paper explores the elegant structure and hidden symmetries of gauge theory scattering amplitudes, especially in N=4 super Yang-Mills, revealing new insights into their mathematical properties and connections to Wilson loops.

Contribution

It demonstrates how BCFW recursion relations solve for tree-level amplitudes and uncovers the large symmetry algebra underlying these invariants.

Findings

Tree-level amplitudes in N=4 super Yang-Mills can be expressed as sums of symmetry invariants.

Connections between scattering amplitudes and Wilson loops are established.

Hidden symmetries significantly constrain the structure of gauge theory amplitudes.

Abstract

These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the BCFW recursion relations we solve for the tree-level S-matrix in N=4 super Yang-Mills theory, and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree-level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.