Families of Quintic Calabi-Yau 3-Folds with Discrete Symmetries

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dc.creatorDoran, Charles
dc.creatorGreene, Brian
dc.creatorJudes, Simon
dc.date2007-01-22
dc.date.accessioned2026-07-07T11:44:02Z
dc.date.available2026-07-07T11:44:02Z
dc.descriptionAt special loci in their moduli spaces, Calabi-Yau manifolds are endowed with discrete symmetries. Over the years, such spaces have been intensely studied and have found a variety of important applications. As string compactifications they are phenomenologically favored, and considerably simplify many important calculations. Mathematically, they provided the framework for the first construction of mirror manifolds, and the resulting rational curve counts. Thus, it is of significant interest to investigate such manifolds further. In this paper, we consider several unexplored loci within familiar families of Calabi-Yau hypersurfaces that have large but unexpected discrete symmetry groups. By deriving, correcting, and generalizing a technique similar to that of Candelas, de la Ossa and Rodriguez-Villegas, we find a calculationally tractable means of finding the Picard-Fuchs equations satisfied by the periods of all 3-forms in these families. To provide a modest point of comparison, we then briefly investigate the relation between the size of the symmetry group along these loci and the number of nonzero Yukawa couplings. We include an introductory exposition of the mathematics involved, intended to be accessible to physicists, in order to make the discussion self-contained.
dc.description54 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/hep-th/0701206
dc.identifierhttp://arxiv.org/abs/hep-th/0701206
dc.identifierCommun.Math.Phys.280:675-725,2008
dc.identifierdoi:10.1007/s00220-008-0473-x
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/201459
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.titleFamilies of Quintic Calabi-Yau 3-Folds with Discrete Symmetries
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