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Mordell-Weil lattice via string junctions. (English) Zbl 1068.81588
Summary: 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.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 14J28 $$K3$$ surfaces and Enriques surfaces 32J81 Applications of compact analytic spaces to the sciences 83E30 String and superstring theories in gravitational theory
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