Geometric Model for Complex Non-Kaehler Manifolds with SU(3) Structure

TL;DR

This paper constructs complex (n+1)-folds as principal holomorphic T2-fibrations over a complex n-fold, focusing on non-Kaehler SU(3)-structures relevant for heterotic string theory compactifications.

Contribution

It provides an explicit geometric construction of non-Kaehler SU(3)-structure manifolds with applications to string theory.

Findings

Identifies a subclass of 3-folds with non-Kaehler SU(3)-structures

Constructs examples with M as K3-surface and 4-torus

Shows these structures satisfy supersymmetry conditions in heterotic theory

Abstract

For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consider the case of M being a Calabi-Yau 2-fold. We show that for such M, there is a subclass of the 3-folds that we construct, which has natural families of non-Kaehler SU(3)-structures satisfying the conditions for N = 1 supersymmetry in the heterotic string theory compactified on the 3-folds. We present examples in the aforementioned subclass with M being a K3-surface and a 4-torus.