A String Deformation of the Parke-Taylor Factor

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 ${\alpha }^{\prime }$ 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 ${\alpha }^{\prime }$ 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.

arXiv comment12+10 pages

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• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
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• CHY Theory for Several Fields