Spacetime foam in twistor string theory

TL;DR

This paper explores the connection between spacetime foam structures in four-dimensional conformal supergravity and twistor spaces with D1 brane charge, proposing a mapping via topological string theory and blowup techniques.

Contribution

It introduces a novel mapping between Kahler spacetime foam and twistor spaces with D1 brane charge, linking gravitational instantons to topological string theory.

Findings

Explicit twistor space constructions for blowups of a2^2.

A meromorphic volume form on these twistor spaces.

A proposed relation to holomorphic superforms on super Calabi-Yau manifolds.

Abstract

We show how a Kahler spacetime foam in four dimensional conformal (super)gravity may be mapped to twistor spaces carrying the D1 brane charge of the B model topological string theory. The spacetime foam is obtained by blowing up an arbitrary number of points in $\C^2$ and can be interpreted as a sum over gravitational instantons. Some twistor spaces for blowups of $\C^2$ are known explicitly. In these cases we write down a meromorphic volume form and suggest a relation to a holomorphic superform on a corresponding super Calabi-Yau manifold.