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

TL;DR

This paper explores a Hamiltonian reduction linking N=2 supersymmetric particle mechanics on complex projective space to motion on a four-sphere with an instanton background, revealing new geometric and supersymmetric structures.

Contribution

It introduces a supersymmetric extension of the Hamiltonian reduction for particles on CP^3, connecting it to superparticle dynamics on S^4 with instantons.

Findings

Established a supersymmetric Hamiltonian reduction framework.

Derived the superfield Lagrangian for the system.

Connected particle mechanics on CP^3 to S^4 with instantons.

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.