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

TL;DR

This paper analyzes constraints on F-theory GUT models with an additional U(1) symmetry, focusing on elliptic fibrations with rational sections and their compatibility with certain singularities.

Contribution

It investigates the conditions on the Tate form coefficients for F-theory GUTs with a Mordell-Weil rank one U(1), linking the presence of U(1) to specific singularities.

Findings

U(1) symmetry is compatible with E6 and E7 singularities.

The study provides conditions on the Tate form coefficients for models with one U(1).

A brief discussion on an E6 x U(1) model is included.

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 ${\cal E}_6$ and ${\cal E}_7$ non-abelian singularities. We briefly comment on a viable ${\cal E}_6\times U(1)$ effective F-theory model.