N=8 mechanics in SU(2) x 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 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 Ar = 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 I D scale invariance. We also find a one-parameter family of scale-invariant q(1,1) actions which, however, are not invariant under the full Ar = 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 Ar = 8, ID supersymmetry. This construction can be generalized to any number of self-interacting q(1,1). (c) 2005 Elsevier B.V. All rights reserved.