Holomorphic Couplings In Non-Perturbative String Compactifications

TL;DR

This paper reviews non-perturbative string compactifications focusing on brane dynamics and holomorphic couplings, deriving effective actions, computing superpotentials, and introducing a geometric framework for five-branes using blow-up threefolds.

Contribution

It introduces a novel geometric approach to describe five-branes via blow-up threefolds and derives exact superpotentials using dualities and Picard-Fuchs equations.

Findings

Derived effective action for D5-branes in Type IIB Calabi-Yau orientifolds

Computed complete perturbative superpotentials from branes and fluxes

Presented a geometric description of five-branes via non-Calabi-Yau blow-up threefolds

Abstract

In this review article we present an analysis of several aspects of four-dimensional, non-perturbative N=1 compactifications of string theory. Our study focuses on brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N=1 effective action, most prominently the superpotential W. This article is divided into three parts. In part one we derive the effective action of a spacetime-filling D5-brane in generic Type IIB Calabi-Yau orientifold compactifications. In the second part we invoke tools from string dualities, namely from F-theory, heterotic/F-theory duality and mirror symmetry, for a more elaborate study of the dynamics of (p,q) 7-branes and heterotic five-branes. In this context we perform exact computations of the complete perturbative effective superpotential, both due to branes and background fluxes. Finally, in the third part we present a novel geometric description of five-branes in Type IIB and heterotic M-theory Calabi-Yau compactifications via a non-Calabi-Yau threefold, that is canonically constructed from the original five-brane and Calabi-Yau threefold via a blow-up. We use this blow-up threefold to derive open-closed Picard-Fuchs differential equations, that govern the complete effective brane and flux superpotential. In addition, we present first evidence to interpret the blow-up threefold as a flux compactification geometrically dual to the original five-brane by defining an SU(3)-structure on it, that is generated dynamically by the five-brane backreaction.