From Twistor String Theory To Recursion Relations

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.

1+11 pages

References in corpus (11)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Perturbative Gauge Theory As A String Theory In Twistor Space
• New Recursion Relations for Tree Amplitudes of Gluons
• MHV Vertices And Tree Amplitudes In Gauge Theory
• On the Tree-Level S-Matrix of Yang-Mills Theory
• The S-Matrix in Twistor Space
• A Googly Amplitude from the B-model in Twistor Space
• Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes
• Parity Invariance For Strings In Twistor Space
• All Googly Amplitudes from the B-model in Twistor Space
• On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes

Cited by in corpus (31)

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• Twistor-Strings, Grassmannians and Leading Singularities
• Gravity in Twistor Space and its Grassmannian Formulation
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
• From 4d Ambitwistor Strings to On Shell Diagrams and Back
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Form factor recursion relations at loop level
• Gluon Tree Amplitudes in Open Twistor String Theory
• Kinematic Numerators and a Double-Copy Formula for N = 4 Super-Yang-Mills Residues
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• The Scattering Variety
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• General Split Helicity Gluon Tree Amplitudes in Open Twistor String Theory
• Yangian in the Twistor String
• The m=2 amplituhedron and the hypersimplex: signs, clusters, triangulations, Eulerian numbers
• Non-Planar On-Shell Diagrams
• New Worldsheet Formulae for Conformal Supergravity Amplitudes
• Analytical amplitudes from numerical solutions of the scattering equations
• A note on NMHV form factors from the Graßmannian and the twistor string
• Ambitwistor strings and reggeon amplitudes in N=4 SYM
• Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D
• Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes