N=4 supersymmetric mechanics with nonlinear chiral supermultiplet
  We construct N=4 supersymmetric mechanics using the N=4 nonlinear chiral supermultiplet. The two bosonic degrees of freedom of this supermultiplet parameterize the sphere S(2) and go into the bosonic components of the standard chiral multiplet when the radius of the sphere goes to infinity. We construct the most general action and demonstrate that the nonlinearity of the supermultiplet results in the deformation of the connection, which couples the fermionic degrees of freedom with the background, and of the bosonic potential. Also a non-zero magnetic field could appear in the system. 
S. Bellucci, A. Beylin, S. Krivonos, A. Nersessian, and E. Orazi