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

References in corpus (8)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Gravity and Yang-Mills Amplitude Relations
• Subleading Soft Factor for String Disk Amplitudes
• Supersymmetry Relations and MHV Amplitudes in Superstring Theory
• Scattering equations and virtuous kinematic numerators and dual-trace functions

Cited by in corpus (13)

• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Subleading Soft Factor for String Disk Amplitudes
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• Relations for Einstein-Yang-Mills amplitudes from the CHY representation
• Chiral Closed strings: Four massless states scattering amplitude
• Ambitwistor Strings: Worldsheet Approaches to perturbative Quantum Field Theories
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• Chiral Superstring and CHY Amplitude
• Infrared behaviour of the one-loop scattering equations and supergravity integrands
• Worldsheet Geometries of Ambitwistor String
• Fermions and the scattering equations
• Sudakov Representation of the Cachazo-He-Yuan Scattering Equations Formalism