Constraints on the BPS Spectrum of N = 2, D = 4 Theories with A-D-E Flavor Symmetry

BPS states of N=2, D=4 Super Yang-Mills theories with ADE flavor symmetry arise as junctions joining a D3-brane to a set of 7-branes defining the enhanced flavor algebra. We show that the familiar BPS spectrum of SU(2) theories with N_f <= 4 is simply given by the set of junctions whose self-intersection is bounded below as required by supersymmetry. This constraint, together with the relations between junction and weight lattices, is used to establish the appearance of arbitrarily large flavor representations for the case of D_{n>=5} and E_n symmetries. Such representations are required by consistency with decoupling down to smaller flavor symmetries.