$T^4$ fibrations over Calabi-Yau two-folds and non-Kahler manifolds in string theory

TL;DR

This paper constructs eight-dimensional non-Kahler manifolds as $T^4$ fibrations over Calabi-Yau two-folds, exploring their geometric properties and relevance in type II string theory with fluxes.

Contribution

It introduces a new geometric model of non-Kahler Hermitian manifolds with $SU(4)$ structure arising from $T^4$ fibrations over Calabi-Yau two-folds in string theory.

Findings

Realization of eight-dimensional manifolds as $T^4$ fibrations over Calabi-Yau two-folds.

Identification of these manifolds as internal spaces with fluxes in type IIB string theory.

Analysis of generalized calibrated cycles within these flux backgrounds.

Abstract

We construct a geometric model of eight-dimensional manifolds and realize them in the context of type II string theory. These eight-manifolds are constructed by non-trivial $T^{4}$ fibrations over Calabi-Yau two-folds. These give rise to eight-dimensional non-Kahler Hermitian manifolds with $SU(4)$ structure. The eight-manifold is also a circle fibration over a seven-dimensional $G_{2}$ manifold with skew torsion. The eight-manifolds of this type appear as internal manifolds with $SU(4)$ structure in type IIB string theory with $F_{3}$ and $F_{7}$ fluxes. These manifolds have generalized calibrated cycles in the presence of fluxes.