Mirror Symmetry in the presence of Branes [Elektronische Ressource] / Adrian Mertens. Betreuer: Christian Römelsberger

Mirror Symmetry in the presence of BranesAdrian MertensMunchen 2011Mirror Symmetry in the presence of BranesAdrian MertensDoktorarbeitan der Fakult at fur Physikder Ludwig{Maximilians{Universit atMunc henvorgelegt vonAdrian Mertensaus Munc henMunc hen, den 17. August 2011Erstgutachter: Prof. Dr. Christian R omelsbergerZweitgutachter: Prof. Dr. Peter MayrTag der mundlic hen Prufung: 11. Oktober 2011ContentsZusammenfassung viiAbstract ixMotivation and Overview xi1 Introduction: Mirror symmetry 11.1 The topological A- and B-model . . . . . . . . . . . . . . . . . . . . . 11.2 The Gauged Linear Sigma Model . . . . . . . . . . . . . . . . . . . . 51.3 Polytopes and the construction of Batyrev . . . . . . . . . . . . . . . 71.4 Picard Fuchs equations and GKZ system . . . . . . . . . . . . . . . . 91.5 The mirror map and correlators . . . . . . . . . . . . . . . . . . . . . 111.6 The inclusion of branes . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Branes with nearly at superpotential 172.1 Geometry and deformation space of the B-model . . . . . . . . . . . . 172.2 Generalized hypergeometric systems for relative periods . . . . . . . . 232.3 Gauss-Manin connection and integrability conditions . . . . . . . . . 282.3.1 Gauss-Manin connection on the open-closed deformation space 282.3.2 Integrability conditions . . . . . . . . . . . . . . . . . . . . . . 322.4 Large radius invariants for the A-model . . . . . . . . . . . . . . . . .