MHV Diagrams from an All-Line Recursion Relation

Abstract

We consider the recursion relation for loop integrands in planar N = 4 SYM generated by an all-line shift of momentum twistors. We examine the behaviour of the rational loop integrands when the shift parameter becomes large, and find that a valid recursion relation may be obtained in all cases. The recursion relation is then formulated both in region momentum space and in momentum twistor space, and solved in detail for some one and two-loop examples. Finally, we show that the general iterative solution of the recursion relation generates the MHV vertex expansion for all loop integrands, providing a proof of the MHV diagram formalism for all loop amplitudes in planar N = 4 SYM.

37 pages

References in corpus (21)

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Cited by in corpus (14)

• A Note on Polytopes for Scattering Amplitudes
• Scattering Amplitudes and Wilson Loops in Twistor Space
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• Massive amplitudes on the Coulomb branch of N=4 SYM
• The Correlahedron
• MHV diagrams in twistor space and the twistor action
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
• Holomorphic Linking, Loop Equations and Scattering Amplitudes in Twistor Space
• Form factor recursion relations at loop level
• Twistor actions for gauge theory and gravity
• Integrands for QCD rational terms and N=4 SYM from massive CSW rules
• The Coulomb-branch S-matrix from massless amplitudes
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes