Scattering Equations and String Theory Amplitudes

Abstract

Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large ${\alpha }^{\prime }$ limit, and whose solution is found algebraically on the surface of solutions to the scattering equations. Because it has support only on the scattering equations, it can be solved exactly, yielding a simple resummed model for ${\alpha }^{\prime }$-corrections to all orders. We use the same idea to generalize scattering equations to amplitudes with fermions and any mixture of scalars, gluons and fermions. In all cases checked we find exact agreement with known results.

v2: 18 pp, 1 figure, added clarifications and comments. Version to be published in PRD

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• New Relations for Gauge-Theory Amplitudes
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Cited by in corpus (51)

• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
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• On the null origin of the ambitwistor string
• Prescriptive Unitarity
• Double Copy from Homotopy Algebras
• Subleading Soft Factor for String Disk Amplitudes
• Integration Rules for Loop Scattering Equations
• Factorization of Chiral String Amplitudes
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• An Algebraic Approach to the Scattering Equations
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• Scattering Equations and Global Duality of Residues
• String amplitudes from field-theory amplitudes and vice versa
• Elimination and recursions in the scattering equations
• Relations for Einstein-Yang-Mills amplitudes from the CHY representation
• Amplitudes for left-handed strings
• General Solution of the Scattering Equations
• Analytic Representations of Yang-Mills Amplitudes
• Comments on the evaluation of massless scattering
• Connected formulas for amplitudes in standard model
• Superstring loop amplitudes from the field theory limit
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• The Polynomial Form of the Scattering Equations is an H-Basis
• Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Ambitwistor Integrands from Tensionless Chiral Superstring Integrands
• Chiral Closed strings: Four massless states scattering amplitude
• Windings of twisted strings
• Ambitwistor Strings: Worldsheet Approaches to perturbative Quantum Field Theories
• On Chiral Splitting and the Ambitwistor String
• One-Loop Yang-Mills Integrands from Scattering Equations
• The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• CHY formula and MHV amplitudes
• A String Deformation of the Parke-Taylor Factor
• On D-brane-Anti D-brane Effective actions and their all order Bulk Singularity Structures
• New Factorization Relations for Non-Linear Sigma Model Amplitudes
• Chiral Superstring and CHY Amplitude
• Four-Gauge-Particle Scattering Amplitudes and Polyakov String Path Integral in the proper-time gauge
• Off-Shell Yang-Mills Amplitude in the CHY Formalism
• Infrared behaviour of the one-loop scattering equations and supergravity integrands
• On All-Order Higher-Point $\text{D}p$-$\overline{\text{D}p}$ Effective Actions
• Permutation in the CHY-Formulation
• All Order ${\alpha }^{\prime }$ Corrections to Fermionic Couplings of D-brane-Anti-D-brane Effective Actions
• All-Order Quartic Couplings in Highly Symmetric D-brane-Anti-D-brane Systems
• CHY-construction of Planar Loop Integrands of Cubic Scalar Theory
• Worldsheet Geometries of Ambitwistor String
• Fermions and the scattering equations
• Sudakov Representation of the Cachazo-He-Yuan Scattering Equations Formalism
• A Novel On-Shell Recursive Relation