MHV Diagrams in Momentum Twistor Space

Abstract

We show that there are remarkable simplifications when the MHV diagram formalism for N=4 super Yang-Mills is reformulated in momentum twistor space. The vertices are replaced by unity while each propagator becomes a dual superconformal `R-invariant' whose arguments may be read off from the diagram. The momentum twistor MHV rules generate a formula for the full, all-loop planar integrand of the super Yang-Mills S-matrix that is manifestly dual superconformally invariant up to the choice of a reference twistor. We give a general proof of this reformulation and illustrate its use by computing the momentum twistor NMHV and NNMHV tree amplitudes and the integrands of the MHV and NMHV 1-loop and the MHV 2-loop planar amplitudes.

36 pages, 13 figures

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• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Notes on the scattering amplitude / Wilson loop duality
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Scattering Amplitudes
• Positive Amplitudes In The Amplituhedron
• Harmony of Super Form Factors
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Scattering Amplitudes and Wilson Loops in Twistor Space
• A Note on Polytopes for Scattering Amplitudes
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
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• An Introduction to On-shell Recursion Relations
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• The Correlahedron
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• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• Tree-Level Formalism
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• Descent equations for superamplitudes
• A dictionary between R-operators, on-shell graphs and Yangian algebras
• Holomorphic Linking, Loop Equations and Scattering Amplitudes in Twistor Space
• Amplitudes of 3d Yang Mills Theory
• OPE for Super Loops
• On Form Factors and Correlation Functions in Twistor Space
• Twistor actions for gauge theory and gravity
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Null Polygonal Wilson Loops in Full N=4 Superspace
• MHV Diagrams from an All-Line Recursion Relation
• Sign Flip Triangulations of the Amplituhedron
• Integrands for QCD rational terms and N=4 SYM from massive CSW rules
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
• Correlation functions of the chiral stress-tensor multiplet in N=4 SYM
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• Basis shape loci and the positive Grassmannian
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• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• Wilson Loop Form Factors: A New Duality
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• A Celestial Description of Planar Super-Yang-Mills Theory
• Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes
• A Tale Of Two Amplitudes In High Energy Physics