Nonlinear (4, 8, 4) Multiplet of N=8, d=1 Supersymmetry
  We construct a nonlinear version of the d=1 off-shell N=8 multiplet (4,8,4), proceeding from a nonlinear realization of the superconformal group OSp(4*|4) in the N=8, d=1 analytic bi-harmonic superspace. The new multiplet is described by a double-charged analytic superfield q^{1,1} subjected to some nonlinear harmonic constraints which are covariant under the OSp(4*|4) transformations. Together with the analytic superspace coordinates, q^{1,1} parametrizes an analytic coset manifold of OSp(4*|4) and so is a Goldstone superfield. In any q^{1,1} action the superconformal symmetry is broken, while N=8, d=1 Poincar\'e supersymmetry can still be preserved. We construct the most general class of such supersymmetric actions and find the general expression for the bosonic target metric in terms of the original analytic Lagrangian superfield density which is thus the target geometry prepotential. It also completely specifies the scalar potential. The metric is conformally flat and, in the SO(4) invariant case, is a deformation of the metric of a four-sphere S^4. 
Evgeny Ivanov