Non-perturbative N=1 strings from geometric singularities

TL;DR

This paper explores the connection between geometric singularities in Calabi-Yau manifolds and supersymmetric quantum field theories, providing a framework for understanding non-perturbative string vacua with five-branes.

Contribution

It introduces a geometric construction that relates singularities to non-perturbative N=1 string vacua, extending previous perturbative models to include five-branes and non-perturbative effects.

Findings

Establishes a relation between Calabi-Yau singularities and supersymmetric QFTs.

Provides a geometric framework for non-perturbative heterotic string vacua.

Extends minimal supersymmetric models to include five-branes and non-perturbative dynamics.

Abstract

The study of curved D-brane geometries in type II strings implies a general relation between local singularities $\cx W$ of Calabi-Yau manifolds and gravity free supersymmetric QFT's. The minimal supersymmetric case is described by F-theory compactifications on $\cx W$ and can be used as a starting point to define minimal supersymmetric heterotic string compactifications on compact Calabi-Yau manifolds with holomorphic, stable gauge backgrounds. The geometric construction generalizes to non-perturbative vacua with five-branes and provides a framework to study non-perturbative dynamics of the heterotic theory.