From Twistor String Theory To Recursion Relations

TL;DR

This paper connects Witten's twistor string theory to recursion relations for scattering amplitudes by deriving a link representation and demonstrating contour deformations that relate the connected prescription to BCFW recursion for N=4 SYM.

Contribution

It derives a new link representation of the twistor string connected prescription and explicitly shows its equivalence to BCFW recursion relations for six and seven particles.

Findings

Link representation relates twistor string to amplitude representations.

Contour deformations transform the connected prescription into BCFW form.

Explicit demonstrations for six and seven particles establish the connection.

Abstract

Witten's twistor string theory gives rise to an enigmatic formula [arXiv:hep-th/0403190] known as the "connected prescription" for tree-level Yang-Mills scattering amplitudes. We derive a link representation for the connected prescription by Fourier transforming it to mixed coordinates in terms of both twistor and dual twistor variables. We show that it can be related to other representations of amplitudes by applying the global residue theorem to deform the contour of integration. For six and seven particles we demonstrate explicitly that certain contour deformations rewrite the connected prescription as the BCFW representation, thereby establishing a concrete link between Witten's twistor string theory and the dual formulation for the S-matrix of N=4 SYM recently proposed by Arkani-Hamed et. al. Other choices of integration contour also give rise to "intermediate prescriptions". We expect a similar though more intricate structure for more general amplitudes.