A Note on Classical Aspects of the Four Dimensional Anomaly-Free Twistor String

TL;DR

This paper explores the classical aspects of an anomaly-free four-dimensional twistor string, extending its definition to curved spaces and linking its classical limit to general relativity, especially for specific spacetime types.

Contribution

It demonstrates the extension of the anomaly-free twistor string to curved twistor space and proposes a connection between its classical limit and general relativity, including simplified models for certain spacetime types.

Findings

Twistor string can be defined in curved twistor space.

Classical limit potentially relates to general relativity.

Simplified models for Petrov type D spacetimes.

Abstract

The recently introduced anomaly-free twistor string in four dimensions is shown to be defined not just in flat but also in curved twistor space. Further, arguments are given that the classical limit of the corresponding string field theory, if it exists, is related to general relativity, in particular to the Isenberg and Yasskin construction using teleparallel gravity. For spacetimes of Petrov type D with two shear-free null congruences the construction can be simplified using two-dimensional twistor manifolds.