CHY formulae in 4d

TL;DR

This paper advances the CHY formalism in four dimensions by developing a reduction method for integrands involving polarization, leading to more efficient 4d CHY formulas using spinors and insights into supersymmetrization.

Contribution

It introduces a general reduction approach for polarization-involved integrands in 4d CHY formulas and constructs more streamlined 4d CHY expressions using spinors.

Findings

Reduced Pfaffian vanishes outside specific solutions

Constructed 4d CHY formulas using spinors

Supersymmetrization is straightforward

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.