WHY TOPOLOGICAL CHARGES IMPLY EXTENDED SUPERSYMMETRY

We present a proof that theories with N = 1 supersymmetry and a conserved topological charge must in fact be invariant under an N = 2 supersymmetry in which the topological charge appears as the central charge. The proof is valid in 2 + 1 and 3 + 1 dimensions. We discuss the more limited results that hold in 1 + 1 dimensions. Additionally, we consider situations in which the existence of instantons signals the presence of N = 2 supersymmetry.