Twistor Spaces, Mirror Symmetry and Self-dual Kahler Manifolds

TL;DR

This paper explores conjectures linking twistor spaces and mirror symmetry, proposing that certain super-Calabi-Yau spaces form mirror pairs and that the B-model on twistor space relates to a 4D gravitational theory involving D1 branes.

Contribution

It provides evidence for two conjectures connecting twistor string theory, mirror symmetry, and 4D gravity, highlighting novel relationships between these areas.

Findings

Super-Calabi-Yau spaces form a mirror pair.

B-model on twistor space relates to 4D gravitational theories.

Partition function involves sum over space-time foams.

Abstract

We present the evidence for two conjectures related to the twistor string. The first conjecture states that two super-Calabi Yaus -- the supertwistor space and the superambitwistor space -- form a mirror pair. The second conjecture is that the B-model on the twistor space can be seen as describing a 4-dimensional gravitational theory, whose partition function should involve a sum over ''space-time foams'' related to D1 branes in the topological string.