A String Deformation of the Parke-Taylor Factor

TL;DR

This work defines a fully $SL(2,C)$-covariant string Parke-Taylor factor $PT_{\alpha'}(\beta)$ through a reduced determinant $det'(\Phi(\sigma,z))$ and embeds it into CHY representations of open string tree amplitudes. Its leading $\alpha'$-term reproduces the field-theory Parke-Taylor factor, enabling a CHY formula for open strings: $A^{open}(\beta) = \int d\mu^{CHY}_n\; PT_{\alpha'}(\beta)\; Pf'\Psi$, while connecting to KLT/Z-theory structures via stringy kernels and abelianizations. The authors establish a covariant construction, derive explicit $\alpha'$-expansions at low multiplicities, and demonstrate how the string Parke-Taylor factor interfaces with open-string CHY integrands and broader string-like models. They also discuss extensions to abelianized and two-disk constructions, and outline future directions including loop Generalizations and ambitwistor-string interpretations.

Abstract

Scattering amplitudes in a range of quantum field theories can be computed using the Cachazo-He-Yuan (CHY) formalism. In theories with colour ordering, the key ingredient is the so-called Parke-Taylor factor. In this note we give a fully $\text{SL}(2,\mathbb{C})$-covariant definition and study the properties of a new integrand called the string Parke-Taylor factor. It has an $α'$ expansion whose leading coefficient is the field-theoretic Parke-Taylor factor. Its main application is that it leads to a CHY formulation of open string tree-level amplitudes. In fact, the definition of the string Parke-Taylor factor was motivated by trying to extend the compact formula for the first $α'$ correction found by He and Zhang, while the main ingredient in its definition is a determinant of a matrix introduced in the context of string theory by Stieberger and Taylor.