Heterotic Non-Kahler Geometries via Polystable Bundles on Calabi-Yau Threefolds

TL;DR

This paper extends previous work to polystable bundles on Calabi-Yau threefolds, constructing explicit examples that enable heterotic flux compactifications with non-Kahler geometries, impacting string theory model building.

Contribution

It generalizes the deformation results to polystable bundles and provides explicit constructions on elliptically fibered Calabi-Yau threefolds.

Findings

Constructed explicit polystable bundles on elliptically fibered Calabi-Yau threefolds.

Demonstrated non-Kahler deformations of three-generation GUT models.

Provided new heterotic flux compactification examples.

Abstract

In arXiv:1008.1018 it is shown that a given stable vector bundle $V$ on a Calabi-Yau threefold $X$ which satisfies $c_2(X)=c_2(V)$ can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case and construct explicit examples of polystable bundles on elliptically fibered Calabi-Yau threefolds where it applies. The polystable bundle is given by a spectral cover bundle, for the visible sector, and a suitably chosen bundle, for the hidden sector. This provides a new class of heterotic flux compactifications via non-Kahler deformation of Calabi-Yau geometries with polystable bundles. As an application, we obtain examples of non-Kahler deformations of some three generation GUT models.