A Direct Proof of BCFW Recursion for Twistor-Strings

TL;DR

This paper provides the first complete proof that twistor-string theory correctly computes all tree-level amplitudes in maximally supersymmetric Yang-Mills theory, using a geometric approach in twistor space.

Contribution

It offers a direct, geometric proof of BCFW recursion in twistor-string theory, linking string path integrals to recursive structures in moduli space.

Findings

Proof that twistor-string path integral obeys BCFW recursion

Geometric interpretation of recursion in twistor space

Connection between boundary divisors and recursive amplitude structures

Abstract

This paper gives a direct proof that the leading trace part of the genus zero twistor-string path integral obeys the BCFW recursion relation. This is the first complete proof that the twistor-string correctly computes all tree amplitudes in maximally supersymmetric Yang-Mills theory. The recursion has a beautiful geometric interpretation in twistor space that closely reflects the structure of BCFW recursion in momentum space, both on the one hand as a relation purely among tree amplitudes with shifted external momenta, and on the other as a relation between tree amplitudes and leading singularities of higher loop amplitudes. The proof works purely at the level of the string path integral and is intimately related to the recursive structure of boundary divisors in the moduli space of stable maps to CP^3.