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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.
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P. Berglund, A. Klemm, P. Mayr, and S. Theisen, “On type IIB vacua with varying coupling constant,” Nucl. Phys. B 558
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M. Fukae, Y. Yamada and S. -K. Yang, “Mordell-Weil lattice via string junctions,” Nucl. Phys. B 572
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2010
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P. Aluffi and M. Esole, “New orientifold weak coupling limits in F-theory,” JHEP 1002
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V. Kumar, D. S. Park and W. Taylor, “6D supergravity without tensor multiplets,” JHEP 1104
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2011
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S. Katz, D. R. Morrison, S. Schafer-Nameki and J. Sully, “Tate’s algorithm and F-theory,” JHEP 1108
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T. Banks, N. Seiberg, “Symmetries and Strings in Field Theory and Gravity,” Phys. Rev. D83
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2012
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D. S. Park, “Anomaly Equations and Intersection Theory,” JHEP 1201
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2012
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D. R. Morrison and W. Taylor, “Matter and singularities,” JHEP 1201
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2012
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