SQM with Non-Abelian Self-Dual Fields: Harmonic Superspace Description

We present a Lagrangian formulation for N=4 supersymmetric quantum-mechanical systems describing the motion in external non-Abelian self-dual gauge fields. For any such system, one can write a component supersymmetric Lagrangian by introducing extra bosonic variables with topological Chern-Simons type interaction. For a special class of such system when the fields are expressed in the `t Hooft ansatz form, it is possible to give a superfield description using harmonic superspace formalism. As a new explicit example, the N=4 mechanics with Yang monopole is constructed.