N=4 superconformal mechanics and the potential structure of AdS spaces

The dynamics of an N=4 spinning particle in a curved background is described using the N=4 superfield formalism. The SU(2)local×SU(2)global N=4 superconformal symmetry of the particle action requires the background to be a real “Kähler-like” manifold whose metric is generated by a sigma-model superpotential. The anti-de-Sitter spaces are shown to belong to this class of manifolds.