A Direct Proof of BCFW Recursion for Twistor-Strings

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.

23 pages, 5 figures

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• Aspects of Scattering Amplitudes and Moduli Space Localization
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• Gravity in Twistor Space and its Grassmannian Formulation
• Twistor Strings for N=8 Supergravity
• MHV diagrams in twistor space and the twistor action
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
• Einstein supergravity amplitudes from twistor-string theory
• All-order celestial OPE in the MHV sector
• Gluon scattering on self-dual radiative gauge fields
• Twistor actions for gauge theory and gravity
• Worldsheet factorization for twistor-strings
• Minitwistors and 3d Yang-Mills-Higgs theory
• On tree amplitudes of supersymmetric Einstein-Yang-Mills theory
• Complete Equivalence Between Gluon Tree Amplitudes in Twistor String Theory and in Gauge Theory
• Yangian in the Twistor String
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• New Formulae for Gravity Amplitudes: Parity Invariance and Soft Limits