Tales of 1001 Gluons

TL;DR

This paper reviews recent advances in calculating tree-level gluon scattering amplitudes in Yang-Mills theories, highlighting methods like recursion, twistor, Grassmannian, and CHY representations, and exploring connections to quantum gravity.

Contribution

It provides a comprehensive overview of modern techniques for computing gluon amplitudes, integrating geometric and algebraic approaches in perturbative quantum field theory.

Findings

Comparison of different amplitude computation methods

Introduction of Grassmannian and amplituhedron frameworks

Discussion on the relation to quantum gravity amplitudes

Abstract

These lectures are centred around tree-level scattering amplitudes in pure Yang-Mills theories, the most prominent example is given by the tree-level gluon amplitudes of QCD. I will discuss several ways of computing these amplitudes, illustrating in this way recent developments in perturbative quantum field theory. Topics covered in these lectures include colour decomposition, spinor and twistor methods, off- and on-shell recursion, MHV amplitudes and MHV expansion, the Grassmannian and the amplituhedron, the scattering equations and the CHY representation. At the end of these lectures there will be an outlook on the relation between pure Yang-Mills amplitudes and scattering amplitudes in perturbative quantum gravity.