On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM

Abstract

We study the relationship between the momentum twistor MHV vertex expansion of planar amplitudes in N=4 super-Yang-Mills and the all-loop generalization of the BCFW recursion relations. We demonstrate explicitly in several examples that the MHV vertex expressions for tree-level amplitudes and loop integrands satisfy the recursion relations. Furthermore, we introduce a rewriting of the MHV expansion in terms of sums over non-crossing partitions and show that this cyclically invariant formula satisfies the recursion relations for all numbers of legs and all loop orders.

34 pages, 17 figures; v2: Minor improvements to exposition and discussion, updated references, typos fixed

References in corpus (15)

• Gluon scattering amplitudes at strong coupling
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Form factors at strong coupling via a Y-system
• All tree-level amplitudes in N=4 SYM
• From Twistor Actions to MHV Diagrams
• Exacting N=4 Superconformal Symmetry
• The Yangian origin of the Grassmannian integral
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• MHV Diagrams in Momentum Twistor Space
• On BCFW shifts of integrands and integrals
• Structure of the MHV-rules Lagrangian
• A Note on Dual MHV Diagrams in N=4 SYM

Cited by in corpus (7)

• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• More on Soft Theorems: Trees, Loops and Strings
• On form factors in N=4 sym
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• Massive On-Shell Supersymmetric Scattering Amplitudes
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes