ON LOCAL F-THEORY GEOMETRIES AND INTERSECTING D7-BRANES

Abstract

We discuss local F-theory geometries and their gauge theory dualities in terms of intersecting D7-branes wrapped four-cycles in Type IIB superstring. The manifolds are built as elliptic K3 surface fibrations over intersecting F0 = CP1 × CP1 base geometry according to ADE Dynkin Diagrams. The base is obtained by blowing up the extended ADE hyper-Kähler singularities of eight-dimensional manifolds considered as sigma model target spaces with eight supercharges. The resulting gauge theory of such local F-theory models are given in terms of Type IIB D7-branes wrapped intersecting F0. The four-dimensional N = 1 anomaly cancelation requirement translates into a condition on the associated affine Lie algebras.