Scattering Amplitudes and BCFW Recursion in Twistor Space

Abstract

Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the three-point seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for $n$-particle MHV and NMHV super-amplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N^2MHV super-amplitude. We also give simple closed form formulae for the N=8 supergravity recursion and the MHV and conjugate MHV amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N^kMHV, the amplitudes are given by 2n-4 integrals in the form of Hilbert transforms of a product of $n-k-2$ purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for tree-level amplitudes in N=4 super Yang-Mills, and we trace their origin to a topological property of split signature space-time. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed, Cachazo, Cheung and Kaplan.

v2: minor corrections + extra refs. v3: further minor corrections, extra discussion of signature issues + more refs

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Cited by in corpus (47)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Gluon Amplitudes as 2d Conformal Correlators
• Unification of Residues and Grassmannian Dualities
• Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory
• Gravity from Rational Curves
• A Twistorial Foundation for the Classical Double Copy
• The Yangian origin of the Grassmannian integral
• Recursion Relations for AdS/CFT Correlators
• $(2,2)$ Scattering and the Celestial Torus
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• MHV Diagrams in Momentum Twistor Space
• On-shell superamplitudes in N<4 SYM
• Local Spacetime Physics from the Grassmannian
• On BCFW shifts of integrands and integrals
• Gravity in Twistor Space and its Grassmannian Formulation
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• Twistor theory at fifty: from contour integrals to twistor strings
• Conformal and Einstein gravity from twistor actions
• Conformal Field Theories in Six-Dimensional Twistor Space
• The Correlahedron
• Ambidextrous light transforms for celestial amplitudes
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• MHV diagrams in twistor space and the twistor action
• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
• Tree-Level Formalism
• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
• Why is the Weyl double copy local in position space?
• A Direct Proof of BCFW Recursion for Twistor-Strings
• Maximal Unitarity for the Four-Mass Double Box
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• Gravity with a cosmological constant from rational curves
• Conformal Higher Spin Theory and Twistor Space Actions
• Soft Gravity by Squaring Soft QED on the Celestial Sphere
• Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes
• Spinor-helicity variables for cosmological horizons in de Sitter space
• Celestial amplitudes in an ambidextrous basis
• Cross-Order Integral Relations from Maximal Cuts
• Worldsheet factorization for twistor-strings
• On the Classification of Residues of the Grassmannian
• Complete Equivalence Between Gluon Tree Amplitudes in Twistor String Theory and in Gauge Theory
• Recursion and worldsheet formulae for 6d superamplitudes
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• Geometric Recursion from Polytope Triangulations and Twisted Homology
• A Celestial Description of Planar Super-Yang-Mills Theory
• Fourier transform from momentum space to twistor space
• Delta functions on twistor space and their sign factors