MHV Diagrams in Momentum Twistor Space
Mathew Bullimore, Lionel Mason, David Skinner

TL;DR
This paper reformulates the MHV diagram formalism for N=4 super Yang-Mills in momentum twistor space, simplifying calculations and making dual superconformal invariance manifest, leading to new formulas for all-loop planar integrands.
Contribution
It introduces a novel momentum twistor space formulation of MHV diagrams that simplifies the computation of super Yang-Mills amplitudes and makes symmetries explicit.
Findings
Simplified MHV diagram rules in momentum twistor space.
Derived formulas for all-loop planar integrands.
Explicit computations of various tree and loop amplitudes.
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.
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