An Introduction to Webs

TL;DR

This paper provides a pedagogical overview of webs, sets of Feynman diagrams relevant to scattering amplitudes in soft radiation limits, highlighting their formal structure and recent computational advances.

Contribution

It introduces the concept of webs, explains their role in exponentiation in gauge theories, and discusses recent progress in calculating web diagrams.

Findings

Webs elucidate the all-order structure of perturbative quantum field theory.

The web mixing matrix formalism advances non-abelian gauge theory calculations.

Recent methods improve the computation of web diagrams.

Abstract

Webs are sets of Feynman diagrams that contribute to the exponents of scattering amplitudes, in the kinematic limit in which emitted radiation is soft. As such, they have a number of phenomenological and formal applications, and offer tantalising glimpses into the all-order structure of perturbative quantum field theory. This article is based on a series of lectures given to graduate students, and aims to provide a pedagogical introduction to webs. Topics covered include exponentiation in (non-)abelian gauge theories, the web mixing matrix formalism for non-abelian gauge theories, and recent progress on the calculation of web diagrams. Problems are included throughout the text, to aid understanding.