The complex null string, Galilean conformal algebra and scattering equations

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.

BMS characters and modular invariance

“…Modular invariance of BMS would be central to understanding this Gross-Mende regime from the point of view of the symmetries on the worldsheet. Intriguingly, it has been recently found that these same BMS 3 symmetries arise in the formulation of the ambi-twistor string [34,35]. Ambitwistor strings [36] are a variant of the original twistor string theory that provide a basis for understanding of the Cachazo-He-Yuan (CHY) formula for scattering of massless fields in quantum field theories [37].…”

“…Ambitwistor strings [36] are a variant of the original twistor string theory that provide a basis for understanding of the Cachazo-He-Yuan (CHY) formula for scattering of massless fields in quantum field theories [37]. Modular invariance of BMS constructed earlier in [25,38] would find its uses here as well, as has been noted in [35].…”

Inhomogeneous tensionless superstrings

“…In [59], it was claimed that the null string and the ambitwistor string are one and the same when one considers a particular quantisation of the null string. There also has been some recent advances [60] where the connections of this null or ambitwistor string to the Cachazo-He-Yuan (CHY) formalism [61] was explored in further detail. See also [62] for further related developments.…”

“…The initial crucial step is defining vertex operators in the 2d GCA and its supersymmetric versions. In the context of the ambitwister string, the authors in [60] noted that the theory had c M = 0. 6 This meant that the symmetry algebra truncates to a single copy of the Virasoro algebra and one can use usual CFT vertex operators.…”

On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring

“…The polarized scattering equation for 6D amplitudes was proposed in [41] while the 11D and 10D polarized scattering equations are among the beautiful findings of [28]. Its relation with ambitwistor string models [42,43,45,46,47,48,49,50,51], the 11D version of which was considered for the first time in [45], was discussed and especially stressed in [28].…”