PLANES, BRANES AND AUTOMORPHISMS II - BRANES IN MOTION

We complete the classification of supersymmetric configurations of two M5-branes, started by Ohta and Townsend. The novel configurations not considered before are those in which the two branes are moving relati ve to one another. These configurations are obtained by starting with two coincident branes and Lorentz-transforming one of them while prese rving some supersymmetry. We completely classify the supersymmetric co nfigurations involving two M5-branes, and interpret them group-theoret ically. We also present some partial results on supersymmetric configu rations involving an arbitrary number of M5-branes. We show that these configurations correspond to Cayley planes in eight-dimensions which are null-rotated relative to each other in the remaining (2 +1) dimens ions. The generic configuration preserves 1/32 of the supersymmetry, b ut other fractions (up to 1/4) are possible by restricting the planes to certain subsets of the Cayley grassmannian. We discuss some example s with larger fractions as well as their associated geometries.