On N=1 Mirror Symmetry for Open Type II Strings

TL;DR

This paper extends mirror symmetry to open N=1 supersymmetric type II string theories with D-branes, providing differential equations, superpotential calculations, and toric geometry methods for analyzing D-brane moduli and phase transitions.

Contribution

It introduces a differential equation framework for open N=1 mirror symmetry, including superpotential computations and a gauged linear sigma model approach.

Findings

Derived flat coordinates and superpotentials for D-branes

Described D-brane phase transitions using toric geometry

Applied methods to various D-brane geometries

Abstract

We study the open string extension of the mirror map for N=1 supersymmetric type II vacua with D-branes on non-compact Calabi-Yau manifolds. Its definition is given in terms of a system of differential equations that annihilate certain period and chain integrals. The solutions describe the flat coordinates on the N=1 parameter space, and the exact disc instanton corrected superpotential on the D-brane world-volume. A gauged linear sigma model for the combined open-closed string system is also given. It allows to use methods of toric geometry to describe D-brane phase transitions and the N=1 K\"ahler cone. Applications to a variety of D-brane geometries are described in some detail.