Mordell-Weil Lattice via String Junctions

Details Mordell-Weil Lattice via String Junctions Mordell-Weil Lattice via String Junctions

1999-09-17

arxiv.org/abs/hep-th/9909122v1

Nucl.Phys. B572 (2000) 71-94

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, Latex, 3 figures

Scientific paper

10.1016/S0550-3213(00)00013-4

We analyze the structure of singularities, Mordell-Weil lattices and torsions of a rational elliptic surface using string junctions in the background of 12 7-branes. The classification of the Mordell-Weil lattices due to Oguiso-Shioda is reproduced in terms of the junction lattice. In this analysis an important role played by the global structure of the surface is observed. It is then found that the torsions in the Mordell-Weil group are generated by the fraction of loop junctions which represent the imaginary roots of the loop algebra $\hat E_9$. From the structure of the Mordell-Weil lattice we find 7-brane configurations which support non-BPS junctions carrying conserved Abelian charges.

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