N=1 Heterotic/F-Theory Duality

TL;DR

This work surveys four-dimensional N=1 heterotic/F-theory duality, detailing how elliptic Calabi–Yau manifolds and stable vector bundles on the heterotic side map to elliptically fibered Calabi–Yau fourfolds on the F-theory side. It develops and compares two bundle-construction frameworks—parabolic and spectral cover—and computes bundle moduli and chiral indices, establishing when c3(V) ≠ 0 and thus nonzero net chirality arises. The analysis confirms precise matching of heterotic fivebranes with F-theory threebranes and demonstrates complete spectrum alignment under non-flux and standard-embedding assumptions, across 8D, 6D, and 4D dualities. It then constructs explicit 4D N=1 models using del Pezzo bases, shows how Z2 modding yields N=1 theories from N=2 parents, and analyzes non-Abelian gauge groups and Higgsing chains to verify duality consistency and to illustrate the richness of the duality web in realistic compactifications.

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.