A First Course on Twistors, Integrability and Gluon Scattering Amplitudes

Abstract

These notes accompany an introductory lecture course on the twistor approach to supersymmetric gauge theories aimed at early-stage PhD students. It was held by the author at the University of Cambridge during the Michaelmas term in 2009. The lectures assume a working knowledge of differential geometry and quantum field theory. No prior knowledge of twistor theory is required.

v2: 118 pages, typos fixed, some clarifications and references added

References in corpus (55)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• A Duality For The S Matrix
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Scattering into the fifth dimension of N=4 super Yang-Mills
• The Grassmannian Origin Of Dual Superconformal Invariance
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• The S-Matrix in Twistor Space
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Consistency Conditions on the S-Matrix of Massless Particles
• All tree-level amplitudes in N=4 SYM
• Unification of Residues and Grassmannian Dualities
• Taming Tree Amplitudes In General Relativity
• From Twistor Actions to MHV Diagrams
• Exacting N=4 Superconformal Symmetry
• Sharpening The Leading Singularity
• Tree Level Recursion Relations In General Relativity
• Yangians, Grassmannians and T-duality
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• On T-Duality and Integrability for Strings on AdS Backgrounds
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• Twistor-Strings, Grassmannians and Leading Singularities
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
• Twistor Actions for Self-Dual Supergravities
• On the fermionic T-duality of the AdS_4 \times CP^3 sigma-model
• Heterotic twistor-string theory
• One-loop phi-MHV amplitudes using the unitarity bootstrap: the general helicity case
• Structure of the MHV-rules Lagrangian
• Unraveling L_{n,k}: Grassmannian Kinematics
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• Symmetries of the N=4 SYM S-matrix
• Twistor transform of all tree amplitudes in N=4 SYM theory
• Generating Charge from Diffeomorphisms
• Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds
• Twistor diagram recursion for all gauge-theoretic tree amplitudes
• A quantization of twistor Yang-Mills theory through the background field method
• Self-Dual Supergravity and Twistor Theory
• MHV Lagrangian for N=4 Super Yang-Mills
• No-scale supersymmetry breaking vacua and soft terms with torsion
• Deriving CSW rules for massive scalar legs and pure Yang-Mills loops
• Scattering amplitudes for eight gauge fields
• Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations
• A super MHV vertex expansion for N=4 SYM theory
• One-loop N=8 Supergravity Amplitudes from MHV Diagrams
• Yang-Mills Theory in Twistor Space
• MHV Lagrangians for Yang--Mills and QCD

Cited by in corpus (26)

• Review of AdS/CFT Integrability: An Overview
• Scattering Amplitudes
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Local temperatures and local terms in modular Hamiltonians
• Goldstone modes and photonization for higher form symmetries
• Twistor theory at fifty: from contour integrals to twistor strings
• An Introduction to On-shell Recursion Relations
• Kinematic Lie Algebras From Twistor Spaces
• Alternative formulations of the twistor double copy
• Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills
• On Twistors and Conformal Field Theories from Six Dimensions
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Conformal Higher Spin Theory and Twistor Space Actions
• $L_{\infty }$-Algebras, the BV Formalism, and Classical Fields
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Higher Gauge Theory
• Field Theory Equivalences as Spans of $L_{\infty }$-algebras
• A Twistor Space Action for Yang-Mills Theory
• Lectures on twistor theory
• On Exact Solvability of $\mathcal{N}$=4 super Yang-Mills
• Hidden Local and Non-local Symmetries of S-matrices of N=2,4,8 SYM in D=2+1
• Explicit Non-Abelian Gerbes with Connections
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• Ambitwistor Yang-Mills Theory Revisited