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arXiv · 1208.2695

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

David R. Morrison·Daniel S. Park
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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.

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David R. Morrison, Daniel S. Park. 2012-11-12. F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds. https://doi.org/10.1007/jhep10(2012)128

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