PLANES, BRANES AND AUTOMORPHISMS I - STATIC BRANES

This is the first of a series of papers devoted to the group-theoretic al analysis of the conditions which must be satisfied for a configurat ion of intersecting M5-branes to be supersymmetric. In this paper we t reat the case of static branes. We start by associating (a maximal tor us of) a different subgroup of Spin(10) with each of the equivalence c lasses of supersymmetric configurations of two M5-branes at angles fou nd by Ohta & Townsend. We then consider configurations of more than tw o intersecting branes. Such a configuration will be supersymmetric if and only if the branes are G-related, where G is a subgroup of Spin(10 ) contained in the isotropy of a spinor. For each such group we determ ine (a lower bound for) the fraction of the supersymmetry which is pre served. We give examples of configurations consisting of an arbitrary number of non-coincident intersecting fivebranes with fractions: 1/32, 1/16, 3/32, 1/8, 5/32, 3/16, and 1/4, and we determine the resulting (calibrated) geometry.