Geometric transitions on non-Kähler manifolds

✍ Scribed by A. Knauf

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 793 KB
• Volume: 55
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/prop.200610332

✦ Synopsis

Abstract

This article is based on the publications [1–3] and the author's PhD‐thesis. We study geometric transitions on the supergravity level using the basic idea of [1], where a pair of non‐Kähler backgrounds was constructed, which are related by a geometric transition. Here we embed this idea into an orientifold setup as suggested in [3]. The non‐Kähler 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‐Kähler 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‐Kähler backgrounds in type I and heterotic theory as proposed in [2]. 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.