Brane Solitons and Hypercomplex Structures

Abstract

The investigation of strings and M-theory involves the understanding of various BPS solitons which in a certain approximation can be thought of as solutions of ten- and eleven-dimensional supergravity theories. These solitons have a brane or a intersecting brane interpretation, saturate a bound and are associated with parallel spinors with respect to a connection of the spin bundle of spacetime. A class of intersecting brane configurations is examined and it is shown that the geometry of spacetime is hyper-K\"ahler with torsion. A relation between these hyper-K\"ahler geometries with torsion and quaternionic calibrations is also demonstrated.