Compactifications of Heterotic Theory on Non-Kahler Complex Manifolds: I

TL;DR

This paper explores new compactifications of heterotic string theory on non-Kahler complex manifolds, revealing their geometric properties, anomaly cancellation, gauge symmetry, and potential for moduli stabilization, which are promising for phenomenology.

Contribution

It introduces a detailed study of non-Kahler compactifications, including geometric analysis, construction of new manifolds, and insights into anomaly cancellation and moduli stabilization.

Findings

Calculation of warp factor and sigma model properties

Natural emergence of anomaly cancellation and gauge symmetry

Potential stabilization of the radial modulus

Abstract

We study new compactifications of the SO(32) heterotic string theory on compact complex non-Kahler manifolds. These manifolds have many interesting features like fewer moduli, torsional constraints, vanishing Euler character and vanishing first Chern class, which make the four-dimensional theory phenomenologically attractive. We take a particular compact example studied earlier and determine various geometrical properties of it. In particular we calculate the warp factor and study the sigma model description of strings propagating on these backgrounds. The anomaly cancellation condition and enhanced gauge symmetry are shown to arise naturally in this framework, if one considers the effect of singularities carefully. We then give a detailed mathematical analysis of these manifolds and construct a large class of them. The existence of a holomorphic (3,0) form is important for the construction. We clarify some of the topological properties of these manifolds and evaluate the Betti numbers. We also determine the superpotential and argue that the radial modulus of these manifolds can actually be stabilized.