On the null origin of the ambitwistor string

TL;DR

This work demonstrates that the Ambitwistor string can be understood as the tensionless (null) limit of the string under a specific quantization scheme and gauge choice. Classically, the null string carries a Galilean Conformal Algebra of constraints, which matches the ambitwistor string, and quantum ambiguities yield two consistent vacua; selecting a particular Ambitwistor gauge makes the null string reproduces the ambitwistor theory, including its spinning version. The authors connect this to the usual tensile string and to HSZ theory, clarifying the emergence of scattering equations and CHY formalism from a tensionless perspective and highlighting implications for moduli spaces and loop measures. The results provide a coherent geometrical picture of how ambitwistor dynamics arise from null-string quantization and motivate further exploration of moduli, supersymmetric extensions, and potential heterotic/open-string generalizations.

Abstract

In this paper we present the null string origin of the ambitwistor string. Classically, the null string is the tensionless limit of string theory, and so too is the Ambitwistor string. Both have as constraint algebra the Galilean Conformal Algebra in two dimensions. But something interesting happens in the quantum theory since there is an ambiguity in quantizing the null string. We show that, given a particular choice of quantization scheme and a particular gauge, the null string coincides with the ambitwistor string both classically and quantum mechanically. We also show that the same holds for the spinning versions of the null string and Ambitwistor string. With these results we clarify the relationship between the Ambitwistor string, the null string, the usual string and the Hohm-Siegel-Zwiebach theory.

Figures (1)

• Figure 1: Diagram that illustrates the ambiguity of the order between the limit $\alpha'\to\infty$ or Gross-Mende limit and quantization.