Abstract
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 supersymmetry. This construction can be generalized to any number of self-interacting q 1 , 1 .
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