Hidden Simplicity 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.

46 pages, 15 figures. v2 ref added, typos fixed

References in corpus (34)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• 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
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• 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
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• All tree-level amplitudes in N=4 SYM
• From correlation functions to scattering amplitudes
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Exacting N=4 Superconformal Symmetry
• Sharpening The Leading Singularity
• Tree Level Recursion Relations In General Relativity
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• The Yangian origin of the Grassmannian integral
• 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
• More on the duality correlators/amplitudes
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Simple loop integrals and amplitudes in N=4 SYM
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Tree-Level Amplitudes in N=8 Supergravity
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Symmetries of the N=4 SYM S-matrix
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory

Cited by in corpus (11)

• Review of AdS/CFT Integrability: An Overview
• Bootstrapping the three-loop hexagon
• One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
• All tree-level amplitudes in massless QCD
• Tree-level Amplitudes in the Nonlinear Sigma Model
• Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization
• Yangians, S-matrices and AdS/CFT
• Susy Theories and QCD: Numerical Approaches
• On-shell supersymmetry for massive multiplets
• Tree-level amplitudes and dual superconformal symmetry
• On R^4 terms and MHV amplitudes in N = 5,6 supergravity vacua of Type II superstrings