Tate’s algorithm for F-theory GUTs with two U(1)s

• Published in: The journal of high energy physics Vol. 2015; no. 3; p. 1
• Main Authors: Lawrie, Craig, Sacco, Damiano
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 10.03.2015; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Elementary Particles; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; F-Theory; Differential and Algebraic Geometry
• ISSN: 1029-8479; 1126-6708; 1127-2236; 1029-8479
• DOI: 10.1007/JHEP03(2015)055

A bstract 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) × 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.