One-dimensional σ-models with N = 5, 6, 7, 8 off-shell supersymmetries

We computed the actions for the 1D N = 5 σ-models with respect to the two inequivalent (2, 8, 6) multiplets. 4 supersymmetry generators are manifest, while the constraint originated by imposing the 5-th supersymmetry automatically induces a full N = 8 off-shell invariance. The resulting action coincides in the two cases and corresponds to a conformally flat 2D target satisfying a special geometry of rigid type. To obtain these results we developed a computational method (for Maple 11) which does not require the notion of superfields and is instead based on the nowadays available list of the inequivalent representations of the 1D N-extended supersymmetry. Its application to systematically analyze the σ-models off-shell invariant actions for the remaining N = 5, 6, 7, 8 (k, 8, 8 - k) multiplets, as well as for the N > 8 representations, only requires more cumbersome computations. (author)