Geometric transitions, topological strings, and generalized complex geometry

Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insight 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-Kahlerity.";In this thesis we demonstrate how to construct a new class of symplectic non-Kahler and complex non-Kahler string theory vacua via geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including supergravity and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kahler and symplectic non-Kahler 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) worldsheet theory with non-trivial H flux turned on. We show that the usual Kahler 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.