Strings in Twistor Superspace and Mirror Symmetry

TL;DR

This paper constructs the super-Landau-Ginzburg mirror of a topological sigma model on a twistor superspace, revealing a geometric interpretation of the mirror and confirming a conjecture relating twistor superspaces.

Contribution

It provides the first explicit construction of the mirror of a sigma model on a twistor superspace and confirms a recent conjecture about their mirror equivalence.

Findings

The super-Landau-Ginzburg mirror is obtained for the twistor superspace sigma model.

The B-model mirror has a clear geometric interpretation.

In a specific limit, the mirror reduces to the twistor superspace CP^{3|4}, confirming the conjecture.

Abstract

We obtain the super-Landau-Ginzburg mirror of the A-twisted topological sigma model on a twistor superspace -- the quadric in CP^{3|3} x CP^{3|3} which is a Calabi-Yau supermanifold. We show that the B-model mirror has a geometric interpretation. In a particular limit for one of the Kaehler parameters of the quadric, we show that the mirror can be interpreted as the twistor superspace CP^{3|4}. This agrees with the recent conjecture of Neitzke and Vafa proposing a mirror equivalence between the two twistor superspaces.