Ambitwistor strings and the scattering equations

Abstract

We show that string theories admit chiral infinite tension analogues in which only the massless parts of the spectrum survive. Geometrically they describe holomorphic maps to spaces of complex null geodesics, known as ambitwistor spaces. They have the standard critical space--time dimensions of string theory (26 in the bosonic case and 10 for the superstring). Quantization leads to the formulae for tree--level scattering amplitudes of massless particles found recently by Cachazo, He and Yuan. These representations localize the vertex operators to solutions of the same equations found by Gross and Mende to govern the behaviour of strings in the limit of high energy, fixed angle scattering. Here, localization to the scattering equations emerges naturally as a consequence of working on ambitwistor space. The worldsheet theory suggests a way to extend these amplitudes to spinor fields and to loop level. We argue that this family of string theories is a natural extension of the existing twistor string theories.

31 pages + refs & appendices

References in corpus (12)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• The Momentum Kernel of Gauge and Gravity Theories
• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
• Conformal Supergravity in Twistor-String Theory
• Scattering in Three Dimensions from Rational Maps
• Parity Invariance For Strings In Twistor Space
• Gravity from Rational Curves
• The Kinematic Algebras from the Scattering Equations
• An ambitwistor Yang-Mills Lagrangian
• Heterotic twistor-string theory
• A new integral formula for supersymmetric scattering amplitudes in three dimensions

Cited by in corpus (224)

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• The Kerr-Schild double copy in curved spacetime
• Celestial amplitudes and conformal soft theorems
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• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• On the null origin of the ambitwistor string
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• Double copy structure of CFT correlators
• A Twistorial Foundation for the Classical Double Copy
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
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• One-loop Scattering Equations and Amplitudes from Forward Limit
• Perturbative gravity at null infinity
• Prescriptive Unitarity
• Color/Kinematics Duality in AdS${}_4$
• Ambitwistor strings at null infinity and subleading soft limits
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Heterotic and bosonic string amplitudes via field theory
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Double Copy from Homotopy Algebras
• Double Copy for Celestial Amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Integration Rules for Loop Scattering Equations
• Gluons and gravitons at one loop from ambitwistor strings
• On the kinematic algebra for BCJ numerators beyond the MHV sector
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• Twin Supergravities from Yang-Mills Squared
• Integration Rules for Scattering Equations
• Factorization of Chiral String Amplitudes
• Scattering Equations and String Theory Amplitudes
• Perturbative gauge theory at null infinity
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
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• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
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• A Worldsheet Theory for Supergravity
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• Celestial double copy from the worldsheet
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• The String Dual to Free $\mathcal{N}=4$ Super Yang-Mills
• Scattering equations and virtuous kinematic numerators and dual-trace functions
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• String amplitudes from field-theory amplitudes and vice versa
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• New Formulas for Amplitudes from Higher-Dimensional Operators
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• The Worldsheet Dual of Free Super Yang-Mills in 4D
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• Cosmological Scattering Equations at Tree-level and One-loop
• General Solution of the Scattering Equations
• MHV scattering of gluons and gravitons in chiral strong fields
• Scattering equations, generating functions and all massless five point tree amplitudes
• Unification of Decoupling Limits in String and M-theory
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Connected formulas for amplitudes in standard model
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• Graviton scattering in self-dual radiative space-times
• CHY Loop Integrands from Holomorphic Forms
• Einstein gravity from the $\mathbb{N}=4$ spinning particle
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Global symmetries of Yang-Mills squared in various dimensions
• A String Theory Which Isn't About Strings
• Gauge $\times$ Gauge on Spheres
• M5-Brane and D-Brane Scattering Amplitudes
• Amplitudes on plane waves from ambitwistor strings
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• Scattering Forms, Worldsheet Forms and Amplitudes from Subspaces
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• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
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• Notes on the ambitwistor pure spinor string
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• Baby Universes and Worldline Field Theories
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• A Superstring Field Theory for Supergravity
• A Combinatoric Shortcut to Evaluate CHY-forms
• CHY formula and MHV amplitudes
• All-multiplicity amplitudes with four massive quarks and identical-helicity gluons
• Twistor Coverings and Feynman Diagrams
• One-loop diagrams with quadratic propagators from the worldsheet
• String-Like Dual Models for Scalar Theories
• Multi-Soft gluon limits and extended current algebras at null-infinity
• A String Deformation of the Parke-Taylor Factor
• A differential operator for integrating one-loop scattering equations
• An analytic superfield formalism for tree superamplitudes in D=10 and D=11
• Spinor description of $D=5$ massless low-spin gauge fields
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Chiral strings, the sectorized description and their integrated vertex operators
• Notes on the $D=11$ pure spinor superparticle
• One loop amplitude from null string
• Supertwistor description of ambitwistor strings
• Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories
• New Factorization Relations for Non-Linear Sigma Model Amplitudes
• Space-time CFTs from the Riemann sphere
• Recursion and worldsheet formulae for 6d superamplitudes
• Bootstrapping solutions of scattering equations
• Ambitwistor Strings in Six and Five Dimensions
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• Fermionic one-loop amplitudes of the RNS superstring
• New Worldsheet Formulae for Conformal Supergravity Amplitudes
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• On-shell type II supergravity from the ambitwistor pure spinor string
• A superfield realization of the integrated vertex operator in an $Ad{S}_5\times S^5$ background
• On differential operators and unifying relations for $1$-loop Feynman integrands
• Ambitwistor String Theory in the Operator Formalism
• Asymmetrically twisted strings
• Basis decompositions of genus-one string integrals
• One-loop integrand from generalised scattering equations
• Dual Non-Lorentzian Backgrounds for Matrix Theories
• On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
• Conformal higher-spin symmetries in twistor string theory
• CHY formulae in 4d
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• Double Soft Theorem for Generalised Biadjoint Scalar Amplitudes
• Off-Shell Yang-Mills Amplitude in the CHY Formalism
• Advanced tools for basis decompositions of genus-one string integrals
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• UV consistency conditions for CHY integrands
• Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms
• New relations for tree-level form factors and scattering amplitudes
• Permutation in the CHY-Formulation
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• Green-Schwarz and Pure Spinor Formulations of Chiral Strings
• Form factors from string amplitudes
• Traversable wormhole for string, but not for particle
• Massless spinning particle and null-string on $Ad{S}_d$: projective-space approach
• Massive strings from a haunted field theory
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• CHY Theory for Several Fields
• From Twistor-Particle Models to Massive Amplitudes
• General relativity as a two-dimensional CFT
• Sudakov Representation of the Cachazo-He-Yuan Scattering Equations Formalism
• Gravitational Scattering in the High-Energy Limit
• On the Spectrum and Spacetime Supersymmetry of Heterotic Ambitwistor String
• Ambitwistor string amplitudes in light-like linear dilaton background
• Geodesic deviation to all orders via a tangent bundle formalism
• On an alternative quantization of R-NS strings
• A Novel On-Shell Recursive Relation