Classification of p-branes, NUTs, waves and intersections

We give a full classification of the multi-charge supersymmetric p-brane solutions in the massless and massive maximal supergravities in dimensions D greater than or equal to 2 obtained from the toroidal reduction of eleven-dimensional supergravity. We derive simple universal rules for determining the fractions of supersymmetry that they preserve, By reversing the steps of dimensional reduction, the p-brane solutions become intersections of p-branes, NUTs and waves in D = 10 or D = 11. Having classified the lower-dimensional p-branes, this provides a classification of all the intersections in D = 10 and D = 11 where the harmonic functions depend on the space transverse to all the individual objects. We also discuss the structure of U-duality multiplets of p-brane solutions, and show how these translate into multiplets of harmonic and Iron-harmonic intersections, (C) 1998 Elsevier Science B.V.