In this thesis, we investigate the behavior of families of lines on one-parameter projective hypersurfaces via the inhomogeneous Picard-Fuchs equation satisfied by the normal functions of the corresponding algebraic cycles. Since the algebraic cycles are geometric invariants, their monodromies around singular loci in the complex structure moduli space provide information about the physics of the underlying variety, i.e. of Calabi-Yau manifolds. In particular, such cycles contribute to the calculation of the D-brane superpotential, with an associated mirror symmetry interpretation. Relations to number theory also arise, as the critical values of the superpotential are found to belong to field extensions of the rationals. Additionally, the contribution to the superpotential may have relevance for the scalar supergravity potential, and hence for the landscape of flux vacua and string phenomenology, which serves as further physics motivation for our study. / Dans cette these, on examine le comportement de familles de droites sur des hypersurfaces projectives a un parametre en passant par l'equation de Picard-Fuchs inhomogene satisfaite par les fonctions normales de cycles algebriques correspondants. Etant donne que les cycles algebriques sont des invariants geometriques, leur monodromie autour des points singuliers dans l'espace des modules de la structure complexe fournit de l'information sur les proprietes physique de la variete sous-jacente, qui est de Calabi-Yau. Notamment, de tels cycles contribuent a l'evaluation du super-potentiel de D-branes, ayant une interpretation en symetrie miroir associee. On trouve egalement des liens avec la theorie des nombres, car les valeurs critiques du superpotentiel se trouvent appartenir a des extensions de corps des nombres rationnels. De plus, la contribution au superpotentiel pourrait s'averer important pour le potentiel scalaire de supergravite, et ainsi pour le paysage des vides de flux et la phenomenologie des cordes, qui est une source de motivation supplementaire pour poursuivre cette etude.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.119712 |
| Date | January 2013 |
| Creators | Jefferson, Robert |
| Contributors | Johannes Walcher (Internal/Supervisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Physics) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | Electronically-submitted theses. |
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