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Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors

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arxiv 1306.0577 v2 pith:4OCBJ674 submitted 2013-06-03 hep-th

Volker Braun , Thomas W. Grimm , Jan Keitel This is my paper · ORCID
classification hep-th
keywords gaugetoricdatafactorspolytopeauxiliarybasecompactification
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An algorithm to systematically construct all Calabi-Yau elliptic fibrations realized as hypersurfaces in a toric ambient space for a given base and gauge group is described. This general method is applied to the particular question of constructing SU(5) GUTs with multiple U(1) gauge factors. The basic data consists of a top over each toric divisor in the base together with compactification data giving the embedding into a reflexive polytope. The allowed choices of compactification data are integral points in an auxiliary polytope. In order to ensure the existence of a low-energy gauge theory, the elliptic fibration must be flat, which is reformulated into conditions on the top and its embedding. In particular, flatness of SU(5) fourfolds imposes additional linear constraints on the auxiliary polytope of compactifications, and is therefore non-generic. Abelian gauge symmetries arising in toric F-theory compactifications are studied systematically. Associated to each top, the toric Mordell-Weil group determining the minimal number of U(1) factors is computed. Furthermore, all SU(5)-tops and their splitting types are determined and used to infer the pattern of U(1) matter charges.

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Cited by 2 Pith papers

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  1. Constraining F-theory Model Building with QCD Axions

    hep-th 2026-05 unverdicted novelty 5.0 of 10

    QCD axions constrain F-theory base threefolds to have rigid or flux-rigidified divisors, yielding typical axion masses around 10^{-9} eV and decay constants near 10^{15} GeV in allowed regions.

  2. F-theory models with $U(1)\times \mathbb{Z}_2,\, \mathbb{Z}_4$ and transitions in discrete gauge groups

    hep-th 2019-08 conditional novelty 4.0 of 10

    On bisection loci in a four-section geometry, the F-theory gauge group enlarges from Z2 to U(1) times Z2, and Higgsing can break it down to a discrete Z4 gauge group.

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