The complex null string, Galilean conformal algebra and scattering equations

TL;DR

This work investigates a gauged-unfixed, complexified null string and its connection to ambitwistor strings by examining its moduli, symmetry algebra (GCA), and an operator formalism for amplitudes. It shows that complexification exposes an ambitwistor-like extra symmetry and that GCA representations truncate to a chiral Virasoro module, explaining spectrum chirality. It provides an explicit operator-based route to tree-level scattering equations and the one-loop partition function, highlighting modular-invariance considerations and the role of an auxiliary modulus in loop dynamics. These results offer a path toward understanding loop-level integration cycles and the incorporation of loop momenta within twistor-like string frameworks, with potential extensions to supersymmetric formulations and other tension regimes.

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.