N=8 mechanics in SU(2)×SU(2) harmonic superspace

The N=8, 1D analytic bi-harmonic superspace is shown to provide a natural setting for N=8 supersymmetric mechanics associated with the off-shell multiplet (4,8,4). The latter is described by an analytic superfield q1,1, and we construct the general superfield and component actions for any number of such multiplets. The set of transformations preserving the flat superspace constraints on q1,1 constitutes N=8 extension of the two-dimensional Heisenberg algebra h(2), with an operator central charge. The corresponding invariant q1,1 action is constructed. It is unique and breaks 1D scale invariance. We also find a one-parameter family of scale-invariant q1,1 actions which, however, are not invariant under the full N=8 Heisenberg supergroup. Based on preserving the bi-harmonic Grassmann analyticity, we formulate N=8, 1D supergravity in terms of the appropriate analytic supervielbeins. For its truncated version we construct, both at the superfield and component levels, the first example of off-shell q1,1 action with local N=8, 1D supersymmetry. This construction can be generalized to any number of self-interacting q1,1.