w∞ algebras, conformal mechanics and black holes

We discuss BPS solitons in gauged N = 2, D = 4 supergravity. The solitons represent extremal black holes interpolating between different vacua of anti-de Sitter spaces. The isometry superalgebras are determined and the motion of a superparticle in the extremal black hole background is studied and confronted with superconformal mechanics. We show that the Virasoro symmetry of conformal mechanics, which describes the dynamics of the superparticle near the horizon of the extremal black hole under consideration, extends to a symmetry under the w(infinity) algebra of area-preserving diffeomorphisms. We find that a Virasoro subalgebra of w(infinity) can be associated with the Virasoro algebra of the asymptotic symmetries of AdS(2). In this way spacetime diffeomorphisms of AdS(2) translate into diffeomorphisms in phase space: our system offers an explicit realization of the AdS(2)/CFT1 correspondence. Using the dimensionally reduced action, the central charge is computed. Finally, we also present generalizations of superconformal mechanics which are invariant under N = 1 and N = 2 superextensions of w(infinity).