Del Pezzo surfaces and affine 7-brane backgrounds

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-bran e configuration is isomorphic to the K-theory group of the corresponding De l 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 S L(2; Z) symmetry of the (E) over cap (9) 7-brane background appears as the Fourier-Mukai transform acting on the D-brane configurations realizing vect or bundles on elliptically fibered B-9.