On topological string theory with Calabi-Yau backgrounds [Elektronische Ressource] / vorgelegt von Babak Haghighat

On Topological String Theory withCalabi-Yau BackgroundsDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen Fakult atderRheinischen Friedrich-Wilhelms-Universit atzu Bonnvorgelegt vonBabak Haghighataus BonnBonn 20092Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakult atder Universit at Bonn.Referent: Prof. Dr. Albrecht KlemmKorreferent: Prof. Dr. Hans-Peter NillesTag der Promotion: 29.10.200923AbstractString theory represents a unifying framework for quantum eld theory as well asfor general relativity combining them into a theory of quantum gravity. The topologicalstring is a subsector of the full string theory capturing physical amplitudes which onlydepend on the topology of the compacti cation manifold. Starting with a review of thephysical applications of topological string theory we go on to give a detailed descriptionof its theoretical framework and mathematical principles. Having this way provided thegrounding for concrete calculations we proceed to solve the theory on three major typesof Calabi-Yau manifolds, namely Grassmannian Calabi-Yau manifolds, local Calabi-Yaumanifolds, and K3 brations. Our method of solution is the integration of the holomorphicanomaly equations and xing the holomorphic ambiguity by physical boundary conditions.We determine the correct parameterization of the ambiguity and new b conditionsat various singularity loci in moduli space.