HKT AND OKT GEOMETRIES ON SOLITON BLACK-HOLE MODULI SPACES

We consider Shiraishi's metrics on the moduli space of extreme black h oles. We interpret the simplification in the pattern of N-body interac tions that he observed in terms of the recent picture of black holes i n four and five dimensions as composites, made up of intersecting bran es. We then show that the geometry of the moduli space of a class of b lack holes in five and nine dimensions is hyper-Kahler with torsion, a nd octonionic-Kahler with torsion, respectively. For this, we examine the geometry of point particle models with extended world-line supersy mmetry and show that both of the above geometries arise naturally in t his context, In addition, we construct a large class of hyper-Kahler w ith torsion and octonionic-Kahler with torsion geometries in various d imensions. We also present a brane interpretation of our results. (C) 1997 Elsevier Science B.V.