N=1 Heterotic/F-Theory Duality

TL;DR

This paper reviews N=1 duality between heterotic string theory and F-theory, detailing the geometric and bundle data calculations, and demonstrating spectrum matching and dual pairs construction.

Contribution

It provides a detailed framework for heterotic/F-theory duality, including explicit Calabi-Yau and bundle data computations and examples with del Pezzo surfaces.

Findings

Matching of chiral multiplet spectra confirmed

Construction of dual pairs with del Pezzo surfaces

Detailed calculations of Calabi-Yau and bundle moduli

Abstract

We review aspects of N=1 duality between the heterotic string and F-theory. After a description of string duality intended for the non-specialist the framework and the constraints for heterotic/F-theory compactifications are presented. The computations of the necessary Calabi-Yau manifold and vector bundle data, involving characteristic classes and bundle moduli, are given in detail. The matching of the spectrum of chiral multiplets and of the number of heterotic five-branes respectively F-theory three-branes, needed for anomaly cancellation in four-dimensional vacua, is pointed out. Several examples of four-dimensional dual pairs are constructed where on both sides the geometry of the involved manifolds relies on del Pezzo surfaces.