An Introduction to Webs

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.

Invited lecture notes for Journal of Physics G. Comments welcome. 42 pages, 19 figures

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• A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
• Topology and Wilson lines: global aspects of the double copy
• Diagrammatic resummation of leading-logarithmic threshold effects at next-to-leading power
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Wilson loops in terms of color invariants
• Classical and quantum gravitational scattering with Generalized Wilson Lines
• Universality-breaking effects in $e^{+}{e}^{-}$ hadronic production processes
• The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory
• Wilson Loops and Integrability
• Boomerang webs up to three-loop order
• CWebGen -- A tool to study colour structure of scattering amplitudes in IR limit