Twistor-Strings, Grassmannians and Leading Singularities

Abstract

We derive a systematic procedure for obtaining an explicit, L-loop leading singularities of planar N=4 super Yang-Mills scattering amplitudes in twistor space directly from their momentum space channel diagrams. The expressions are given as integrals over the moduli of connected, nodal curves in twistor space whose degree and genus matches expectations from twistor-string theory. We propose that a twistor-string theory for pure N=4 super Yang-Mills, if it exists, is determined by the condition that these leading singularity formulae arise as residues when an unphysical contour for the path integral is used, by analogy with the momentum space leading singularity conjecture. We go on to show that the genus g twistor-string moduli space for g-loop N^{k-2}MHV amplitudes may be mapped into the Grassmannian G(k,n). Restricting to a leading singularity, the image of this map is a 2(n-2)-dimensional subcycle of G(k,n) of exactly the type found from the Grassmannian residue formula of Arkani-Hamed, Cachazo, Cheung and Kaplan. Based on this correspondence and the Grassmannian conjecture, we deduce restrictions on the possible leading singularities of multi-loop N^pMHV amplitudes. In particular, we argue that no new leading singularities can arise beyond 3p loops.

50 pages, 20 figures. Section 2.5 extended, errors in 5.2 corrected, new section 5.3 inserted, references added. In all, 5 new diagrams and 5 extra pages

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Cited by in corpus (49)

• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Gravity as the Square of Gauge Theory
• Towards a Basis for Planar Two-Loop Integrals
• Unification of Residues and Grassmannian Dualities
• Maximal Unitarity at Two Loops
• Scattering Amplitudes
• Generalized Unitarity and Six-Dimensional Helicity
• Yangians, Grassmannians and T-duality
• The Yangian origin of the Grassmannian integral
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Superconformal invariants for scattering amplitudes in N=4 SYM theory
• Local Spacetime Physics from the Grassmannian
• Gravity in Twistor Space and its Grassmannian Formulation
• Simple loop integrals and amplitudes in N=4 SYM
• An Introduction to On-shell Recursion Relations
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• Unraveling L_{n,k}: Grassmannian Kinematics
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• MHV diagrams in twistor space and the twistor action
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• Susy Theories and QCD: Numerical Approaches
• Positroids, Plabic Graphs, and Scattering Amplitudes in Mathematica
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• Multi-Parton Scattering Amplitudes via On-Shell Methods
• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
• Descent equations for superamplitudes
• Einstein supergravity amplitudes from twistor-string theory
• From 4d Ambitwistor Strings to On Shell Diagrams and Back
• A Direct Proof of BCFW Recursion for Twistor-Strings
• A Grassmannian Etude in NMHV Minors
• A new integral formula for supersymmetric scattering amplitudes in three dimensions
• On Soft Theorems And Form Factors In N=4 SYM Theory
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Inverse Soft Factors and Grassmannian Residues
• Cross-Order Integral Relations from Maximal Cuts
• Worldsheet factorization for twistor-strings
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Some analytic results for two-loop scattering amplitudes
• On the Classification of Residues of the Grassmannian
• Scattering amplitudes at strong coupling for 4K gluons
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Recursion and worldsheet formulae for 6d superamplitudes
• The m=2 amplituhedron and the hypersimplex: signs, clusters, triangulations, Eulerian numbers
• Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
• Parity Symmetry and Soft Limit for the Cachazo-Geyer Gravity Amplitude
• A Celestial Description of Planar Super-Yang-Mills Theory
• Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes