The complex null string, Galilean conformal algebra and scattering equations

TL;DR

This paper investigates the null string's complexification, gauge fixing, and amplitude calculations, revealing connections to ambitwistor strings and Galilean conformal algebra, aiming to deepen understanding of scattering equations and loop expansions.

Contribution

It introduces a detailed analysis of the null string's symmetries, gauge fixing, and amplitude computation, linking these to ambitwistor strings and the Galilean conformal algebra.

Findings

Complexification links null string to ambitwistor string

Operator formalism enables tree-level amplitude calculations

Results suggest new insights into loop expansions in twistor-like models

Abstract

The scattering equation formalism for scattering amplitudes, and its stringy incarnation, the ambitwistor string, remains a mysterious construction. In this paper, we pursue the study a gauged-unfixed version of the ambitwistor string known as the null string. We explore the following three aspects in detail; its complexification, gauge fixing, and amplitudes. We first study the complexification of the string; the associated symmetries and moduli, and connection to the ambitwistor string. We then look in more details at the leftover symmetry algebra of the string, called Galilean conformal algebra; we study its local and global action and gauge-fixing. We finish by presenting an operator formalism, that we use to compute tree-level scattering amplitudes based on the scattering equations and a one-loop partition function. These results hopefully will open the way to understand conceptual questions related to the loop expansion in these twistor-like string models.