Spacetime foam in twistor string theory

Abstract

We show how a Kähler 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 $\mathbb{C}^2$ and can be interpreted as a sum over gravitational instantons. Some twistor spaces for blowups of $\mathbb{C}^2$ 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.