Holomorphic N=1 Special Geometry of Open--Closed Type II Strings

TL;DR

This paper introduces a new geometric framework called holomorphic N=1 special geometry that extends the familiar special geometry of N=2 theories to analyze superpotentials in certain flux and brane configurations in type II string compactifications on Calabi-Yau threefolds.

Contribution

It develops the concept of holomorphic N=1 special geometry, providing a unified approach to compute superpotentials in N=1 string theories, extending methods from N=2 special geometry.

Findings

Defines holomorphic N=1 special geometry structure

Relates superpotential computation to mirror symmetry techniques

Provides a foundation for explicit instanton correction calculations

Abstract

We outline a general geometric structure that underlies the N=1 superpotentials of a certain class of flux and brane configurations in type II string compactifications on Calabi-Yau threefolds. This ``holomorphic N=1 special geometry'' is in many respects comparable to, and in a sense an extension of, the familiar special geometry in N=2 supersymmetric type II string compactifications. It puts the computation of the instanton-corrected superpotential W of the four-dimensional N=1 string effective action on a very similar footing as the familiar computation of the N=2 prepotential F via mirror symmetry. In this note we present some of the main ideas and results, while more details as well as some explicit computations will appear in a companion paper