String dualities and superpotential [Elektronische Ressource] / vorgelegt von Tae-Won Ha

String dualitiesandsuperpotentialDissertationzurErlangungdesDoktorgrades(Dr.rer.nat.)derMathematisch-NaturwissenschaftlichenFakulatätderRheinischenFriedrich-Wilhelms-UniversitätzuBonnvorgelegtvonTae-Won HaausCheong-Ju,Chung-Buk,SüdkoreaBonn 2010Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultät der Uni-versitätBonn.1.Gutachter: Prof.Dr.AlbrechtKlemm2.Gutachter: PD.Dr.StefanFörsteTagderPromotion: 16.Juli2010Erscheinungsjahr: 2010AbstractThe main objective of this thesis is the computation of the superpotential induced by D5-branes in the type IIB string theory and by five-branes in the heterotic string theory. Bothsuperpotentialshavethesamefunctionalformwhichisthechainintegraloftheholomorphicthree-form. Usingrelative(co)homology we canunifythefluxandbranesuperpotential. ThechainintegralcanbeseenasanexampleoftheAbel-Jacobimap. Wediscussmanystructuressuch as mixed Hodge structure which allows for the computation of Picard-Fuchs differen-tial equations crucial for explicit computations. We blow up the Calabi-Yau threefold alongthe submanifold wrapped by the brane to obtain geometrically more appropriate configura-tion. Theresultinggeometryisnon-Calabi-Yauandwe havea canonically givendivisor. Thisblown-up geometrymakesit possible torestrictourattentiontocomplex structuredeforma-tions.