N=1 Dual String Pairs and their Modular Superpotentials

TL;DR

This paper reviews dualities between heterotic and F-theory string vacua with N=1 supersymmetry, focusing on dual pairs in various dimensions, matching spectra, and superpotentials through geometric and index calculations.

Contribution

It provides a detailed analysis of dual string pairs, matching spectra and superpotentials, and introduces methods to compute heterotic bundle moduli and F-theory spectra.

Findings

Massless spectra of dual pairs agree via index formulas.

Superpotentials match for specific heterotic/F-theory pairs.

Hodge numbers determine F-theory spectra and moduli counts.

Abstract

We review the duality between heterotic and F--theory string vacua with N=1 space-time supersymmetry in eight, six and four dimensions. In particular, we discuss two chains of four-dimensional F--theory/heterotic dual string pairs, where F--theory is compactified on certain elliptic Calabi-Yau fourfolds, and the dual heterotic vacua are given by compactifications on elliptic Calabi-Yau threefolds plus the specification of the $E_8\times E_8$ gauge bundles. We show that the massless spectra of the dual pairs agree by using, for one chain of models, an index formula to count the heterotic bundle moduli and determine the dual F--theory spectra from the Hodge numbers of the fourfolds and of the type IIB base spaces. Moreover as a further check, we demonstrate that for one particular heterotic/F--theory dual pair the N=1 superpotentials are the same.