Geometric Transitions, Topological Strings, and Generalized Complex Geometry

Chuang, Wu-yen ; /SLAC /Stanford U., Phys. Dept.

Stanford Linear Accelerator Center

关键词: Symmetry;    Compactification;    Geometry;    Targets Theory-Hep,Hepth;    Instantons;   

DOI  :  10.2172/909289
RP-ID  :  SLAC-R-873
RP-ID  :  AC02-76SF00515
RP-ID  :  909289

美国|英语

来源: UNT Digital Library

【 摘 要 】

Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism.