Mordell-Weil torsion and the global structure of gauge groups in F-theory

• Verfasst von: Mayrhofer, Christoph [VerfasserIn]
• Verfasst von: Till, Oskar [VerfasserIn]
• Verfasst von: Weigand, Timo [VerfasserIn]
• Titel: Mordell-Weil torsion and the global structure of gauge groups in F-theory
• Verf.angabe: Christoph Mayrhofer, David R. Morrison, Oskar Till and Timo Weigand
• Fussnoten: Gesehen am 19.12.2017
• Titel Quelle: Enthalten in: De.arxiv.org
• Jahr Quelle: 2014
• Band/Heft Quelle: (2014) Artikel-Nummer 1405.3656, 43 Seiten
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1566524369

Abstract

We study the global structure of the gauge group $G$ of F-theory compactified on an elliptic fibration $Y$. The global properties of $G$ are encoded in the torsion subgroup of the Mordell-Weil group of rational sections of $Y$. Generalising the Shioda map to torsional sections we construct a specific integer divisor class on $Y$ as a fractional linear combination of the resolution divisors associated with the Cartan subalgebra of $G$. This divisor class can be interpreted as an element of the refined coweight lattice of the gauge group. As a result, the spectrum of admissible matter representations is strongly constrained and the gauge group is non-simply connected. We exemplify our results by a detailed analysis of the general elliptic fibration with Mordell-Weil group $\mathbb Z_2$ and $\mathbb Z_3$ as well as a further specialization to $\mathbb Z \oplus \mathbb Z_2$. Our analysis exploits the representation of these fibrations as hypersurfaces in toric geometry.