Topological string theory, modularity and non-perturbative physics [Elektronische Ressource] / Marco Rauch

Topological string theory, modularityand non-perturbative physicsDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen Fakult¨atderRheinischen Friedrich-Wilhelms-Universit¨at Bonnvorgelegt vonMarco RauchausMemmingenBonn 2011Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakult¨atder Rheinischen Friedrich-Wilhelms-Universita¨t Bonn.1. Gutachter: Prof. Dr. Albrecht Klemm2. Gutachter: PD Dr. Stefan F¨orsteTag der Promotion: 19. September 2011Erscheinungsjahr: 2011ABSTRACTIn this thesis the holomorphic anomaly of correlators in topological string theory, matrixmodels and supersymmetric gauge theories is investigated. In the first part it is shown howthe techniques of direct integration known from topological string theory can be used to solvethe closed amplitudes of Hermitian multi-cut matrix models with polynomial potentials. Inthe case of the cubic matrix model, explicit expressions for the ring of non-holomorphicmodular forms that are needed to express all closed matrix model amplitudes are given. Thisallows to integrate the holomorphic anomaly equation up to holomorphic modular terms thatare fixed by the gap condition up to genus four. There is an one-dimensional submanifold ofthe moduli space in which the spectral curve becomes the Seiberg–Witten curve and the ringreduces to the non-holomorphic modular ring of the group Γ(2).