Planes, Branes and Automorphisms I. Static Branes

This is the first of a series of papers devoted to the group-theoretical analysis of the conditions which must be satisfied for a configuration of intersecting M5-branes to be supersymmetric. In this paper we treat the case of static branes. We start by associating (a maximal torus of) a different subgroup of Spin 10 with each of the equivalence classes of supersymmetric configurations of two M5-branes at angles found by Ohta & Townsend. We then consider configurations of more than two intersecting branes. Such a configuration will be supersymmetric if and only if the branes are G-related, where G is a subgroup of Spin10 contained in the isotropy of a spinor. For each such group we determine (a lower bound for) the fraction of the supersymmetry which is preserved. We give examples of configurations consisting of an arbitrary number of non-coincident intersecting fivebranes with fractions: 1 32 , 1 16 ,