Mirror symmetry for open strings

TL;DR

This paper explores how superpotentials in type IIA string theory with D6-branes are generated by disc instantons, providing explicit examples and a preliminary mirror map for open string moduli.

Contribution

It demonstrates the existence of instanton effects from special Lagrangian cycles and constructs a mirror map for open string moduli in Calabi-Yau compactifications.

Findings

Examples of special Lagrangian three-cycles with nontrivial topology are mirror to obstructed rational curves.

Explicit disc instanton configurations ending on these cycles are provided.

A preliminary mirror map for open string moduli is constructed in the large-radius limit.

Abstract

We discuss the generation of superpotentials in four-dimensional, N = 1 supersymmetric field theories arising from type IIA D6-branes wrapped on supersymmetric three-cycles of a Calabi-Yau threefold. In general, nontrivial superpotentials arise from sums over disc instantons. We find several examples of special Lagrangian three-cycles with nontrivial topology which are mirror to obstructed rational curves, conclusively demonstrating the existence of such instanton effects. In addition, we present explicit examples of disc instantons ending on the relevant three-cycles. Finally, we give a preliminary construction of a mirror map for the open string moduli, in a large-radius limit of the type IIA compactification.