Geometric Transitions on non-Kaehler Manifolds

TL;DR

This paper explores geometric transitions on non-Kaehler manifolds within supergravity, demonstrating their properties, constructing new backgrounds via dualities, and analyzing their structures and relations across string theories.

Contribution

It embeds geometric transition ideas into orientifold setups, constructs new non-Kaehler backgrounds in various string theories, and provides a local toy model consistent with flux and torsional relations.

Findings

Non-Kaehler backgrounds are non half-flat but admit local symplectic structures.

New non-Kaehler backgrounds are constructed via T- and S-duality.

A global heterotic solution similar to Maldacena-Nunez is proposed.

Abstract

This article is based on the author's PhD--thesis. We study geometric transitions on the supergravity level using the basic idea of arXiv:hep-th/0403288, where a pair of non-Kaehler backgrounds was constructed, which are related by a geometric transition. Here we embed this idea into an orientifold setup as suggested in arXiv:hep-th/0511099. The non-Kaehler backgrounds we obtain in type IIA are non-trivially fibered due to their construction from IIB via T-duality with Neveu-Schwarz flux. We demonstrate that these non-Kaehler manifolds are not half-flat and show that a symplectic structure exists on them at least locally. We also review the construction of new non-Kaehler backgrounds in type I and heterotic theory as proposed in arXiv:hep-th/0408192. They are found by a series of T- and S-duality and can be argued to be related by geometric transitions as well. A local toy model is provided that fulfills the flux equations of motion in IIB and the torsional relation in heterotic theory, and that is consistent with the U-duality relating both theories. For the heterotic theory we also propose a global solution that fulfills the torsional relation because it is similar to the Maldacena-Nunez background.