Schoen manifold with line bundles as resolved magnetized orbifolds

TL;DR

This paper presents an alternative description of the Schoen manifold as a blow-up of a Z2xZ2 orbifold with roto-translation, demonstrating how magnetized tori enable chirality in heterotic string compactifications and constructing a realistic GUT model.

Contribution

It introduces a new geometric perspective on the Schoen manifold and shows how magnetized tori can recover chirality, including explicit model construction and modifications to spectrum formulas.

Findings

Chirality is achieved via magnetized tori in the Schoen manifold.

Constructed an E8xE8' heterotic SU(5) GUT with three generations.

Proposed modifications to heterotic orbifold spectrum formulas in magnetized scenarios.

Abstract

We give an alternative description of the Schoen manifold as the blow-up of a Z2xZ2 orbifold in which one Z2 factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained in heterotic string compactifications using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an E8xE8' heterotic SU(5) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard heterotic orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non--perturbative heterotic models by Aldazabal et al. we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.