Scattering Equations, Twistor-string Formulas and Double-soft Limits in Four Dimensions

Abstract

We study scattering equations and formulas for tree amplitudes of various theories in four dimensions, in terms of spinor helicity variables and on-shell superspace for supersymmetric theories. As originally obtained in Witten's twistor string theory and other twistor-string models, the equations can take either polynomial or rational forms, and we clarify the simple relation between them. We present new, four-dimensional formulas for all tree amplitudes in the non-linear sigma model, a special Galileon theory and the maximally supersymmetric completion of the Dirac-Born-Infeld theory. Furthermore, we apply the formulas to study various double-soft theorems in these theories, including the emissions of a pair of soft photons, fermions and scalars for super-amplitudes in super-DBI theory.

22 pages, 2 tables; v2: ref added, minor typos fixed

References in corpus (4)

• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Ambitwistor strings in 4-dimensions
• Gravity from Rational Curves
• Unification of Galileon Dualities

Cited by in corpus (44)

• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions
• Logarithmic Terms in the Soft Expansion in Four Dimensions
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• Gravity Waves from Soft Theorem in General Dimensions
• Subleading Soft Theorem for Multiple Soft Gravitons
• Inverse of the String Theory KLT Kernel
• UV considerations on scattering amplitudes in a web of theories
• New Formulas for Amplitudes from Higher-Dimensional Operators
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• Connected formulas for amplitudes in standard model
• Notes on Scattering Amplitudes as Differential Forms
• CHY Loop Integrands from Holomorphic Forms
• Collinear limits beyond the leading order from the scattering equations
• M5-Brane and D-Brane Scattering Amplitudes
• A note on connected formula for form factors
• The connected prescription for form factors in twistor space
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• Double Soft Theorem for Perturbative Gravity
• The momentum amplituhedron of SYM and ABJM from twistor-string maps
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Testing Subleading Multiple Soft Graviton Theorem for CHY Prescription
• Double-copy towards supergravity inflation with $\alpha$-attractor models
• Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian
• Effective observables for electromagnetic duality from novel amplitude decomposition
• Origin of Soft Limits from Nonlinear Supersymmetry in Volkov-Akulov Theory
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Nonlinear (Super)Symmetries and Amplitudes
• A String Deformation of the Parke-Taylor Factor
• Soft Theorems from Compactification
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• Bootstrapping solutions of scattering equations
• Leading soft theorem for multiple gravitini
• Leading order multi-soft behaviors of tree amplitudes in NLSM
• CHY formulae in 4d
• Leading multi-soft limits from scattering equations
• Multi-Regge kinematics and the scattering equations
• Tree amplitudes from nonlinear (super)symmetries in Volkov-Akulov theory
• Characterizing the solutions to scattering equations that support tree-level ${\text{N}}^k\text{MHV}$ gauge/gravity amplitudes
• A note on multi-trace EYM amplitudes in four dimensions
• Gravitational Scattering in the High-Energy Limit