F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds

Abstract

The Mordell-Weil group of an elliptically fibered Calabi-Yau threefold X contains information about the abelian sector of the six-dimensional theory obtained by compactifying F-theory on X. After examining features of the abelian anomaly coefficient matrix and U(1) charge quantization conditions of general F-theory vacua, we study Calabi-Yau threefolds with Mordell-Weil rank-one as a first step towards understanding the features of the Mordell-Weil group of threefolds in more detail. In particular, we generate an interesting class of F-theory models with U(1) gauge symmetry that have matter with both charges 1 and 2. The anomaly equations --- which relate the Neron-Tate height of a section to intersection numbers between the section and fibral rational curves of the manifold --- serve as an important tool in our analysis.

29 pages + appendices, 5 figures; v2: minor corrections

References in corpus (4)

• Global aspects of the space of 6D N = 1 supergravities
• 6D supergravity without tensor multiplets
• Hypercharge Flux, Exotics, and Anomaly Cancellation in F-theory GUTs
• Massive U(1)s and Heterotic Five-Branes on K3

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• Non-Higgsable QCD and the Standard Model Spectrum in F-theory
• Multiple Fibrations in Calabi-Yau Geometry and String Dualities
• F-GUTs with Mordell-Weil U(1)'s
• Tall sections from non-minimal transformations
• Generic matter representations in 6D supergravity theories
• Tate's Algorithm for F-theory GUTs with two U(1)s
• Discrete gauge groups in certain F-theory models in six dimensions
• Tools for CICYs in F-theory
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