Fluxes in F-theory Compactifications on Genus-One Fibrations

TL;DR

This paper develops methods to construct gauge fluxes in F-theory on genus-one fibrations with multi-sections, revealing conditions for anomaly cancellation and flux quantization in models with discrete gauge symmetries.

Contribution

It generalizes transversality conditions for gauge fluxes to genus-one fibrations with multi-sections and demonstrates their application in anomaly-free SU(5) x Z2 models.

Findings

Constructed vertical gauge fluxes in a bisection model with SU(5) x Z2

Showed non-abelian anomalies vanish in these models

Identified arithmetic constraints on intersection numbers for flux quantization

Abstract

We initiate the construction of gauge fluxes in F-theory compactifications on genus-one fibrations which only have a multi-section as opposed to a section. F-theory on such spaces gives rise to discrete gauge symmetries in the effective action. We generalize the transversality conditions on gauge fluxes known for elliptic fibrations by taking into account the properties of the available multi-section. We test these general conditions by constructing all vertical gauge fluxes in a bisection model with gauge group SU(5) x Z2. The non-abelian anomalies are shown to vanish. These flux solutions are dynamically related to fluxes on a fibration with gauge group SU(5) x U(1) by a conifold transition. Considerations of flux quantization reveal an arithmetic constraint on certain intersection numbers on the base which must necessarily be satisfied in a smooth geometry. Combined with the proposed transversality conditions on the fluxes these conditions are shown to imply cancellation of the discrete Z2 gauge anomalies as required by general consistency considerations.