N=1 Dual String Pairs and their Massless Spectra

TL;DR

This paper constructs dual string pairs with N=1 supersymmetry using del Pezzo surfaces, matching their massless spectra through geometric and index-based methods, advancing understanding of string dualities.

Contribution

It introduces two chains of N=1 dual string pairs with geometries based on del Pezzo surfaces and provides a method to match their massless spectra.

Findings

Successful construction of dual string pairs with matching spectra

Use of index formulas to count heterotic bundle moduli

Matching spectra via Hodge numbers of fourfolds and base spaces

Abstract

We construct two chains of fourdimensional F-theory/heterotic dual string pairs with N=1 supersymmetry. On the F-theory side as well as on the heterotic side the geometry of the involved manifolds relies on del Pezzo surfaces. We match the massless spectra 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 $X^4$ and of the type IIB base spaces.