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Journal of High Energy Physics

, 2015:144 | Cite as

F-theory and all things rational: surveying U(1) symmetries with rational sections

  • Craig LawrieEmail author
  • Sakura Schäfer-Nameki
  • Jin-Mann Wong
Open Access
Regular Article - Theoretical Physics

Abstract

We study elliptic fibrations for F-theory compactifications realizing 4d and 6d supersymmetric gauge theories with abelian gauge factors. In the fibration these U(1) symmetries are realized in terms of additional rational section. We obtain a universal characterization of all the possible U(1) charges of matter fields by determining the corresponding codimension two fibers with rational sections. In view of modelling supersymmetric Grand Unified Theories, one of the main examples that we analyze are U(1) symmetries for SU(5) gauge theories with \( \overline{\mathbf{5}} \) and 10 matter. We use a combination of constraints on the normal bundle of rational curves in Calabi-Yau three- and four-folds, as well as the splitting of rational curves in the fibers in codimension two, to determine the possible configurations of smooth rational sections. This analysis straightforwardly generalizes to multiple U(1)s. We study the flops of such fibers, as well as some of the Yukawa couplings in codimension three. Furthermore, we carry out a universal study of the U(1)-charged GUT singlets, including their KK-charges, and determine all realizations of singlet fibers. By giving vacuum expectation values to these singlets, we propose a systematic way to analyze the Higgsing of U(1)s to discrete gauge symmetries in F-theory.

Keywords

F-Theory Differential and Algebraic Geometry 

Notes

Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Craig Lawrie
    • 1
    Email author
  • Sakura Schäfer-Nameki
    • 1
  • Jin-Mann Wong
    • 1
  1. 1.Department of MathematicsKing’s College LondonLondonUnited Kingdom

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