Mordell-Weil torsion in the mirror of multi-sections

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dc.contributor.authorOehlmann, Paul-Konstantinen
dc.contributor.authorReuter, Jonasen
dc.contributor.authorSchimannek, Thorstenen
dc.contributor.departmentPhysicsen
dc.date.accessioned2019-03-01T20:17:51Zen
dc.date.available2019-03-01T20:17:51Zen
dc.date.issued2016-12-12en
dc.description.abstractWe give further evidence that genus-one fibers with multi-sections are mirror dual to fibers with Mordell-Weil torsion. In the physics of F-theory compactifications this implies a relation between models with a non-simply connected gauge group and those with discrete symmetries. We provide a combinatorial explanation of this phenomenon for toric hypersurfaces. In particular this leads to a criterion to deduce Mordell-Weil torsion directly from the polytope. For all 3134 complete intersection genus-one curves in three-dimensional toric ambient spaces we confirm the conjecture by explicit calculation. We comment on several new features of these models: the Weierstrass forms of many models can be identified by relabeling the coefficient sections. This reduces the number of models to 1024 inequivalent ones. We give an example of a fiber which contains only non-toric sections one of which becomes toric when the fiber is realized in a different ambient space. Similarly a singularity in codimension one can have a toric resolution in one representation while it is non-toric in another. Finally we give a list of 24 inequivalent genus-one fibers that simultaneously exhibit multi-sections and Mordell-Weil torsion in the Jacobian. We discuss a self-mirror example from this list in detail.en
dc.description.notesWe would like to thank Hans Jockers and Albrecht Klemm for useful discussions. The work of P.O., J.R. and T.S. is partially supported by a scholarship of the Bonn-Cologne Graduate School BCGS, the SFB-Transregio TR33 The Dark Universe (Deutsche Forschungsgemeinschaft) and the European Union 7th network program Unification in the LHC era (PITN-GA-2009-237920). The work of Paul Oehlmann is also supported in part by NSF grant PHY-1417337 and NSF grant PHY-1417316. J.R. would like to thank CERN for hospitality during the completion of this work. P.O. would like to thank KIAS for hospitality and finanical support the completion of this work.en
dc.description.sponsorshipBonn-Cologne Graduate School BCGSen
dc.description.sponsorshipDeutsche Forschungsgemeinschaft [SFB-Transregio TR33]en
dc.description.sponsorshipEuropean Union [PITN-GA-2009-237920]en
dc.description.sponsorshipNSF [PHY-1417337, PHY-1417316]en
dc.description.sponsorshipKIASen
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1007/JHEP12(2016)031en
dc.identifier.issn1029-8479en
dc.identifier.issue12en
dc.identifier.other31en
dc.identifier.urihttp://hdl.handle.net/10919/88045en
dc.language.isoen_USen
dc.publisherSpringeren
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectDifferential and Algebraic Geometryen
dc.subjectF-Theoryen
dc.subjectGlobal Symmetriesen
dc.subjectString Dualityen
dc.titleMordell-Weil torsion in the mirror of multi-sectionsen
dc.title.serialJournal of High Energy Physicsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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