2012/08/31 by David R. Morrison, Daniel S. Park
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep10(2012)128
published as JHEP 1210:128,2012 · 29 pages + appendices, 5 figures; v2: minor corrections
arxiv created 2012/11/12 · arxiv updated 2012/11/13
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.