Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes

Abstract

Using twistor space intuition, Cachazo, Svrcek and Witten presented novel diagrammatic rules for gauge-theory amplitudes, expressed in terms of maximally helicity-violating (MHV) vertices. We define non-MHV vertices, and show how to use them to give a recursive construction of these amplitudes. We also use them to illustrate the equivalence of various twistor-space prescriptions, and to determine the associated combinatoric factors.

28 pages, 13 figures, ReVTeX; updated references, cosmetic changes to figures, minor changes to text

References in corpus (22)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• Massive Loop Amplitudes from Unitarity
• Progress in One-Loop QCD Computations
• On the Tree-Level S-Matrix of Yang-Mills Theory
• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
• Two-Loop g -> gg Splitting Amplitudes in QCD
• One-Loop Corrections to Two-Quark Three-Gluon Amplitudes
• A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
• Matching Higher Conserved Charges for Strings and Spins
• Tree Amplitudes in Gauge Theory as Scalar MHV Diagrams
• A Googly Amplitude from the B-model in Twistor Space
• The Googly Amplitudes in Gauge Theory
• Cubic Twistorial String Field Theory
• All Googly Amplitudes from the B-model in Twistor Space
• Unitarity-based Techniques for One-Loop Calculations in QCD

Cited by in corpus (70)

• New Recursion Relations for Tree Amplitudes of Gluons
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• A direct proof of the CSW rules
• Recursion Relations for Gauge Theory Amplitudes with Massive Particles
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• Non-Supersymmetric Loop Amplitudes and MHV Vertices
• Basics of Generalized Unitarity
• MHV Vertices and Fermionic Scattering Amplitudes in Gauge Theory with Quarks and Gluinos
• The Last of the Finite Loop Amplitudes in QCD
• A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory
• All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• Color-dressed recursive relations for multi-parton amplitudes
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
• One-Loop MHV Amplitudes in Supersymmetric Gauge Theories
• Lectures on Twistor Strings and Perturbative Yang-Mills Theory
• Recursive Calculation of One-Loop QCD Integral Coefficients
• Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
• Recursion Relations for Tree Amplitudes in Super Gauge Theories
• Gravity, Twistors and the MHV Formalism
• Dissolving N=4 loop amplitudes into QCD tree amplitudes
• MHV-Vertices for Gravity Amplitudes
• MHV Rules for Higgs Plus Multi-Parton Amplitudes
• Twistor-Inspired Construction of Electroweak Vector Boson Currents
• Multi-Gluon Collinear Limits from MHV diagrams
• Twistor-Strings, Grassmannians and Leading Singularities
• MHV Diagrams in Momentum Twistor Space
• From Trees to Loops and Back
• From Yang-Mills Lagrangian to MHV Diagrams
• Amplitudes in the beta-deformed Conformal Yang-Mills
• All Split Helicity Tree-Level Gluon Amplitudes
• Compact Formulas for Tree Amplitudes of Six Partons
• Scalar diagrammatic rules for Born amplitudes in QCD
• SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• A comparison of efficient methods for the computation of Born gluon amplitudes
• From Twistor String Theory To Recursion Relations
• The rational parts of one-loop QCD amplitudes I: The general formalism
• Structure of the MHV-rules Lagrangian
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings
• Collinear Limits in QCD from MHV Rules
• A Note on MHV Amplitudes for Gravitons
• Coplanarity In Twistor Space Of N=4 Next-To-MHV One-Loop Amplitude Coefficients
• Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos
• Twistor transform of all tree amplitudes in N=4 SYM theory
• Tree-Level Formalism
• Six-Quark Amplitudes from Fermionic MHV Vertices
• Orbifolding the Twistor String
• The Topological B-Model on Fattened Complex Manifolds and Subsectors of N=4 Self-Dual Yang-Mills Theory
• S-Matrix Equivalence Theorem Evasion and Dimensional Regularisation with the Canonical MHV Lagrangian
• Systematics of One-Loop Scattering Amplitudes in N=4 Super Yang-Mills Theories
• Gauge Theory Amplitudes, Scalar Graphs and Twistor Space
• Sign Flip Triangulations of the Amplituhedron
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Comments on MHV Tree Amplitudes for Conformal Supergravitons from Topological B-Model
• (Non)-supersymmetric Marginal Deformations from Twistor String Theory
• On-Shell Unitarity Bootstrap for QCD Amplitudes
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• Noncommutative mechanics, Landau levels, twistors and Yang-Mills amplitudes
• Developments in perturbative QCD
• On perturbative field theory and twistor string theory
• Recursive structures in string field theory
• Born amplitudes in QCD from scalar diagrams
• Cachazo-Svrcek-Witten Rules for Tree-Level Gluonic Amplitudes Revisited
• Quantum MHV Diagrams