Tate's Algorithm for F-theory GUTs with two U(1)s

TL;DR

This paper systematically studies elliptic fibrations with two U(1) symmetries in F-theory, introducing new SU(5) x U(1)^2 models with multiple charged matter representations using Tate's algorithm.

Contribution

It introduces a new class of SU(5) x U(1)^2 fibrations with multiple charged matter, expanding the toolkit for F-theory GUT model building.

Findings

Identified fibers with specializations beyond vanishing orders.

Constructed a table of Tate-like forms for fibers with two U(1)s.

Developed models with multiple 10 matter representations.

Abstract

We present a systematic study of elliptic fibrations for F-theory realizations of gauge theories with two U(1) factors. In particular, we determine a new class of SU(5) x U(1)^2 fibrations, which can be used to engineer Grand Unified Theories, with multiple, differently charged, 10 matter representations. To determine these models we apply Tate's algorithm to elliptic fibrations with two U(1) symmetries, which are realized in terms of a cubic in P^2. In the process, we find fibers which are not characterized solely in terms of vanishing orders, but with some additional specialization, which plays a key role in the construction of these novel SU(5) models with multiple 10 matter. We also determine a table of Tate-like forms for Kodaira fibers with two U(1)s.