CHY formulae in 4d

Abstract

In this paper, we develop a rather general way to reduce integrands with polarization involved in the Cachazo-He-Yuan formulae, such as the reduced Pfaffian, its compactiffcation and its squeezing, as well as the new object for F^3 amplitude. We prove that the reduced Pfaffian vanishes unless evaluated on a certain set of solutions. It leads us to build up the 4d CHY formulae using spinors, which strains off many useless solutions. The supersymmetrization is straightforward and may provide a hint to understand ambitwistor string in 4d.

typos fixed

References in corpus (19)

• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Ambitwistor strings in 4-dimensions
• Subleading soft theorem in arbitrary dimension from scattering equations
• One-loop amplitudes on the Riemann sphere
• Gravity from Rational Curves
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Scattering Equations, Twistor-string Formulas and Double-soft Limits in Four Dimensions
• New Formulas for Amplitudes from Higher-Dimensional Operators
• Connected formulas for amplitudes in standard model
• One-loop Amplitudes in Six-Dimensional (1,1) Theories from Generalised Unitarity
• A note on connected formula for form factors
• Scattering Equations: Real Solutions and Particles on a Line
• The connected prescription for form factors in twistor space

Cited by in corpus (6)

• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• A String Deformation of the Parke-Taylor Factor
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• Off-Shell Yang-Mills Amplitude in the CHY Formalism
• Pfaffian Diagrams for Gluon Tree Amplitudes