In extended 4-dimensional theories with N=2 supersymmetry, corresponding to a single Dirac spinor supercharge, the conditions are stronger. The N=2 supersymmetry algebra contains two representations with scalars, the vector multiplet which contains a complex scalar and the hypermultiplet which contains two complex scalars. The moduli space of the vector multiplets is called the Coulomb branch while that of the hypermultiplets is called the Higgs branch. The total moduli space is locally a product of these two branches, as nonrenormalization theorems imply that the metric of each is independent of the fields of the other multiplet.(See for example Argyres, Non-Perturbative Dynamics Of Four-Dimensional Supersymmetric Field Theories, pp. 6–7, for further discussion of the local product structure.)