IN SU ( 2 ) xSU ( 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 q 1,1 , 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 q 1,1 constitutes N =8 extension of the two-dimensional Heisenberg algebra h(2) , with an operator central charge. The corresponding invariant q 1,1 action is constructed. It is unique and breaks 1D scale invariance. We also find a one-parameter family of scale-invariant q 1,1 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 q 1,1 action with local N =8 , 1D supersym-metry. This construction can be generalized to any number of self-interacting q 1,1 .