F-theory on Genus-One Fibrations

• Published in: arXiv.org
• Main Authors: Braun, Volker, Morrison, David R
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 26.03.2014
• Subjects: Branes; Dilatons; Hyperspaces; M theory; Mathematics - Algebraic Geometry; Physics - High Energy Physics - Theory; Representations
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1401.7844

We argue that M-theory compactified on an arbitrary genus-one fibration, that is, an elliptic fibration which need not have a section, always has an F-theory limit when the area of the genus-one fiber approaches zero. Such genus-one fibrations can be easily constructed as toric hypersurfaces, and various \(SU(5)\times U(1)^n\) and \(E_6\) models are presented as examples. To each genus-one fibration one can associate a \(\tau\)-function on the base as well as an \(SL(2,\mathbb{Z})\) representation which together define the IIB axio-dilaton and 7-brane content of the theory. The set of genus-one fibrations with the same \(\tau\)-function and \(SL(2,\mathbb{Z})\) representation, known as the Tate-Shafarevich group, supplies an important degree of freedom in the corresponding F-theory model which has not been studied carefully until now. Six-dimensional anomaly cancellation as well as Witten's zero-mode count on wrapped branes both imply corrections to the usual F-theory dictionary for some of these models. In particular, neutral hypermultiplets which are localized at codimension-two fibers can arise. (All previous known examples of localized hypermultiplets were charged under the gauge group of the theory.) Finally, in the absence of a section some novel monodromies of Kodaira fibers are allowed which lead to new breaking patterns of non-Abelian gauge groups.