N=2 supersymmetric S^2 -> CP^3 -> S^4 fibration viewed as superparticle mechanics

Abstract

We discuss a Hamiltonian reduction procedure that relates the mechanics of an N=2 particle on CP^3 with the motion of such a superparticle on S^4 in the presence of an instanton background. The key ingredients of the bosonic fibration S^2 -> CP^3 -> S^4 are recalled from the viewpoint of particle mechanics on CP^3. We describe an N=2 supersymmetric extension which allows for a Hamiltonian reduction. The S^2 degrees of freedom are encoded in the supercharges via SU(2) currents. Finally, we present the Hamiltonian of our system and its superfield Lagrangian.