Non-Kaehler String Backgrounds and their Five Torsion Classes

TL;DR

This paper analyzes six-dimensional non-Kähler manifolds with SU(3) structures, classifying their torsion and demonstrating the Iwasawa manifold as a supersymmetric heterotic background with non-zero H-field.

Contribution

It provides a detailed classification of torsion classes for non-Kähler manifolds in string compactifications and explicitly relates these to supersymmetry conditions.

Findings

Identifies five torsion classes for SU(3) structures in non-Kähler manifolds.

Establishes a dictionary between torsion classes and supersymmetry conditions.

Shows the Iwasawa manifold as a valid heterotic supersymmetric background with non-zero H-field.

Abstract

We discuss the mathematical properties of six--dimensional non--K\"ahler manifolds which occur in the context of ${\cal N}=1$ supersymmetric heterotic and type IIA string compactifications with non--vanishing background H--field. The intrinsic torsion of the associated SU(3) structures falls into five different classes. For heterotic compactifications we present an explicit dictionary between the supersymmetry conditions and these five torsion classes. We show that the non--Ricci flat Iwasawa manifold solves the supersymmetry conditions with non--zero H--field, so that it is a consistent heterotic supersymmetric groundstate.