F-GUTs with Mordell-Weil U(1)'s

Abstract

In this note we study the constraints on F-theory GUTs with extra $U(1)$'s in the context of elliptic fibrations with rational sections. We consider the simplest case of one abelian factor (Mordell-Weil rank one) and investigate the conditions that are induced on the coefficients of its Tate form. Converting the equation representing the generic hypersurface $P_{112}$ to this Tate's form we find that the presence of a U(1), already in this local description, is consistent with the exceptional ${\mathcal{E}}_6$ and ${\mathcal{E}}_7$ non-abelian singularities. We briefly comment on a viable ${\mathcal{E}}_6\times U(1)$ effective F-theory model.

13 pages

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Cited by in corpus (7)

• Tall sections from non-minimal transformations
• Non-Higgsable abelian gauge symmetry and F-theory on fiber products of rational elliptic surfaces
• Discrete gauge groups in certain F-theory models in six dimensions
• 6D SCFTs and Gravity
• $\frac{1}{2}$ Calabi-Yau 3-folds, Calabi-Yau 3-folds as double covers, and F-theory with U(1)s
• Orders of Vanishing and U(1) Charges in F-theory
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV