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Fluxes in F-theory Compactifications on Genus-One Fibrations

Ling Lin, Christoph Mayrhofer, Oskar Till, Timo Weigand

TL;DR

The paper develops a systematic framework for constructing and constraining $G_4$ gauge fluxes in F-theory on genus-one fibrations without a section, focusing on a bisection with gauge group $SU(5)\times\mathbb{Z}_2$ and its conifold-related $SU(5)\times U(1)$ phase. It generalizes the transversality conditions to multi-section settings, builds horizontal and vertical fluxes, and expresses flux data via matter surfaces, enabling explicit chirality computations and anomaly checks. Across a conifold transition, the authors demonstrate a consistent flux map that preserves D3-charge and chiral indices, and they uncover an arithmetic constraint on base intersections tied to flux quantization that also enforces cancellation of discrete $\mathbb{Z}_2$ anomalies. The results extend the established flux program to genus-one fibrations, illuminate the role of discrete symmetries in F-theory, and point toward future work on higher-degree multi-sections and vector-like spectra in such backgrounds.

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.

Fluxes in F-theory Compactifications on Genus-One Fibrations

TL;DR

The paper develops a systematic framework for constructing and constraining gauge fluxes in F-theory on genus-one fibrations without a section, focusing on a bisection with gauge group and its conifold-related phase. It generalizes the transversality conditions to multi-section settings, builds horizontal and vertical fluxes, and expresses flux data via matter surfaces, enabling explicit chirality computations and anomaly checks. Across a conifold transition, the authors demonstrate a consistent flux map that preserves D3-charge and chiral indices, and they uncover an arithmetic constraint on base intersections tied to flux quantization that also enforces cancellation of discrete anomalies. The results extend the established flux program to genus-one fibrations, illuminate the role of discrete symmetries in F-theory, and point toward future work on higher-degree multi-sections and vector-like spectra in such backgrounds.

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.

Paper Structure

This paper contains 24 sections, 92 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Fluxes on a $\mathbb P_{112}[4]$-fibration with a bisection
  3. The transversality condition for multi-section fibrations
  4. A genus-one fibration with gauge group $SU(5) \times \mathbb Z_2$
  5. Horizontal and all vertical fluxes in the $SU(5) \times \mathbb Z_2$ model
  6. Fluxes from matter surfaces
  7. The ${\bf{{\bar{10}}}}$ Surface
  8. The ${\bf{{\bar{5}}}^A}$ Surface
  9. The ${\bf{{\bar{5}}}^B}$ Surface
  10. Chiralities and non-abelian anomalies
  11. All vertical fluxes on a ${\rm Bl}^1 \mathbb P_{112}[4]$-fibration
  12. All vertical fluxes
  13. Fluxes from matter surfaces
  14. The ${\bf{{\bar{10}}_{2}}}$ surface
  15. The ${\bf{{{5}}_{-6}}}$ surface
  16. ...and 9 more sections

Figures (2)

  • Figure 1: The matter curves on the $SU(5)$ divisor $\{\theta = 0\}$ and the Yukawa couplings involving the $SU(5)$ charged matter in codimension three.
  • Figure 2: The matter curves in the $SU(5)$ divisor $\{\theta = 0\}$ and the Yukawa couplings involving the $SU(5)$ charged matter in codimension three.