Elliptic fibrations for SU(5) x U(1) x U(1) F-theory vacua

TL;DR

This paper constructs elliptic Calabi-Yau fibrations with Mordell-Weil rank two for F-theory compactifications, systematically classifying SU(5) x U(1) x U(1) gauge symmetries and analyzing their geometric and physical properties.

Contribution

It introduces a systematic framework for constructing and analyzing elliptic fibrations with two abelian gauge factors in F-theory, including explicit models and their matter spectra.

Findings

Constructed elliptic fibrations with Mordell-Weil rank two.

Classified SU(5) x U(1) x U(1) gauge models using tops.

Analyzed matter curves, charges, and Yukawa couplings.

Abstract

Elliptic Calabi-Yau fibrations with Mordell-Weil group of rank two are constructed. Such geometries are the basis for F-theory compactifications with two abelian gauge groups in addition to non-abelian gauge symmetry. We present the elliptic fibre both as a Bl^2P^2[3]-fibration and in the birationally equivalent Weierstrass form. The spectrum of charged singlets and their Yukawa interactions are worked out in generality. This framework can be combined with the toric construction of tops to implement additional non-abelian gauge groups. We utilise the classification of tops to construct SU(5) x U(1) x U(1) gauge symmetries systematically and study the resulting geometries, presenting the defining equations, the matter curves and their charges, the Yukawa couplings and explaining the process in detail for an example. Brane recombination relates these geometries to a Bl^1P^2[3]-fibration with a corresponding class of SU(5) x U(1) models. We also present the SU(5) tops based on the elliptic fibre Bl^1P_[1,1,2][4], corresponding to another class of SU(5) x U(1) models.