MHV Diagrams in Momentum Twistor Space

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.