Del Pezzo Surfaces and Affine 7-brane Backgrounds

Details Del Pezzo Surfaces and Affine 7-brane Backgrounds Del Pezzo Surfaces and Affine 7-brane Backgrounds

1999-10-06

arxiv.org/abs/hep-th/9910054v2

JHEP 0001 (2000) 043

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LaTeX, 2 eps figures. v2: minor changes, version to appear in JHEP

Scientific paper

10.1088/1126-6708/2000/01/043

A map between string junctions in the affine 7-brane backgrounds and vector bundles on del Pezzo surfaces is constructed using mirror symmetry. It is shown that the lattice of string junctions with support on an affine 7-brane configuration is isomorphic to the K-theory group of the corresponding del Pezzo surface. This isomorphism allows us to construct a map between the states of the N=2, D=4 theories with E_N global symmetry realized in two different ways in Type IIB and Type IIA string theory. A subgroup of the SL(2,Z) symmetry of the \hat{E}_9 7-brane background appears as the Fourier-Mukai transform acting on the D-brane configurations realizing vector bundles on elliptically fibered B_9.

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