The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space

TL;DR

This paper proposes that the complete planar S-matrix of N=4 super Yang-Mills theory can be represented as a supersymmetric Wilson loop in twistor space, unifying amplitude calculations with Wilson loop correlators.

Contribution

It introduces a novel twistor space Wilson loop framework that captures all N^kMHV amplitudes at all loops, connecting classical and quantum aspects of the S-matrix.

Findings

Explicit computations match known amplitude expressions

Correlation functions in twistor space reproduce MHV rules

Planar duals of MHV diagrams emerge naturally in the framework

Abstract

We propose that the complete planar S-matrix of N=4 super Yang-Mills - including all N^kMHV partial amplitudes to all loops - is equivalent to the correlation function of a supersymmetric Wilson loop in twistor space. Remarkably, the entire classical S-matrix arises from evaluating the correlation function in the self-dual sector, while the expansion of the correlation function in powers of the Yang-Mills coupling constant provides the loop expansion of the amplitudes. We support our proposal with explicit computations of the n particle NMHV and NNMHV trees, the integrands of the 1-loop MHV and NMHV amplitudes, and the n particle 2-loop MHV amplitude. These calculations are performed using the twistor action in axial gauge. In this gauge, the Feynman diagrams of the correlation function are the planar duals of the usual MHV diagrams for the scattering amplitude. The results are presented in the form of a sum of products of dual superconformal invariants in (momentum) twistor space, and agree with the expressions derived in arXiv:1009.1854 directly from the MHV rules. The twistor space Wilson loop is a natural supersymmetric generalization of the standard Wilson loop used to compute MHV amplitudes. We show how the Penrose-Ward transform can be used to determine a corresponding supersymmetrization on space-time.