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Geometric transitions on non‐Kähler manifolds
Author(s) -
Knauf A.
Publication year - 2007
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200610332
Subject(s) - orientifold , heterotic string theory , supergravity , fibered knot , symplectic geometry , duality (order theory) , type (biology) , physics , m theory , f theory , theoretical physics , pure mathematics , relation (database) , mathematical physics , mathematics , supersymmetry , brane cosmology , database , computer science , ecology , biology
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.