HyperKähler manifolds & multiply-intersecting branes

Abstract

This is a summary of the work in the author's recent paper with this title written with Jerome Gauntlett, George Papadopoulos and Paul Townsend, hep-th/97022012. We showed how to construct hyper-Kähler 8-metrics in terms of arrangements of three-dimensional hyperplanes in six-dimensional euclidean space. The slopes of the planes define two relatively prime intgers (p,q). Under reduction to ten dimensions and T-duality we get a geometric picture of the action of SL(2,$\text{Z}$) on the (NS ⊗ NS, qR ⊗ R) 5-branes of type IIB string theory. Configurations are exhibited with $\text{3}\text{16}\text{'}\text{th}$ SUSY.