String Vacua with N=2 Supersymmetry in Four Dimensions

TL;DR

This paper reviews four-dimensional string vacua with N=2 supersymmetry, exploring dualities, spectra, non-perturbative phenomena, and black hole solutions in heterotic and type II string theories.

Contribution

It provides a comprehensive comparison of heterotic and type II N=2 string compactifications, including dualities, spectra, non-perturbative effects, and black hole entropy calculations.

Findings

Agreement of massless spectra in dual string pairs

Matching of prepotentials and gravitational couplings in weak coupling limit

Black hole entropies depend on Calabi-Yau topological data

Abstract

In this article we review four-dimensional string vacua with N=2 space-time supersymmetry. In particular, we will discuss several aspects of the string-string duality between the heterotic string, compactified on $K3\times T^2$, and the type II superstring compactified on a Calabi-Yau three-fold. We investigate the massless supersymmetric spectra, showing agreement for a large class of dual heterotic/type II string pairs. Some emphasis is given to non-perturbative heterotic phenomena, such as non-perturbative transitions among different vacua and strong coupling singularities, and to their geometric Calabi-Yau description on the type II side. We compare the effective N=2 supergravity actions of dual heterotic/type II string compactifications, and show that the N=2 prepotentials and also higher order gravitational couplings nicely agree in the weak heterotic coupling limit. Finally we consider extremal black hole solutions of N=2 supergravity which arise in the context of heterotic or type II N=2 compactifications. For the type II backgrounds we show how the entropies of these black holes depend on the topological data of the underlying Calabi-Yau spaces; we also construct massless black holes which are relevant for the conifold transition among different Calabi-Yau vacua.