U(1) symmetries in F-theory GUTs with multiple sections

TL;DR

This paper systematically constructs F-theory GUT models with multiple U(1) symmetries, detailing their geometric origin, fluxes, and Yukawa interactions, revealing new singlet states and couplings beyond local models.

Contribution

It introduces a general formalism for F-theory models with up to four U(1) factors, focusing on SU(5) GUTs, and explores their geometric and physical properties in detail.

Findings

Construction of models with up to four U(1) factors

Identification of extra SU(5)-singlet states

Discovery of new Yukawa couplings involving singlets

Abstract

We present a systematic construction of F-theory compactifications with Abelian gauge symmetries in addition to a non-Abelian gauge group G. The formalism is generally applicable to models in global Tate form but we focus on the phenomenologically interesting case of G=SU(5). The Abelian gauge factors arise due to extra global sections resulting from a specific factorisation of the Tate polynomial which describes the elliptic fibration. These constructions, which accommodate up to four different U(1) factors, are worked out in detail for the two possible embeddings of a single U(1) factor into E8, usually denoted SU(5) x U(1)_X and SU(5) x U(1)_PQ. The resolved models can be understood either patchwise via a small resolution or in terms of a P_{1,1,2}[4] description of the elliptic fibration. We derive the U(1) charges of the fields from the geometry, construct the U(1) gauge fluxes and exemplify the structure of the Yukawa interaction points. A particularly interesting result is that the global SU(5) x U(1)_PQ model exhibits extra SU(5)-singlet states which are incompatible with a single global decomposition of the 248 of E8. The states in turn lead to new Yukawa type couplings which have not been considered in local model building.