New model of N=8 superconformal mechanics

Using an N=4, d=1 superfield approach, we construct an N=8 supersymmetric action of the self-interacting off-shell N=8 multiplet (1,8,7). This action is found to be invariant under the exceptional N=8,d=1 superconformal group F(4) with the R-symmetry subgroup SO(7). The general N=8 supersymmetric (1,8,7) action is a sum of the superconformal action and the previously known free bilinear action. We show that the general action is also superconformal, but with respect to redefined superfield transformation laws. The scalar potential can be generated by two Fayet-Iliopoulos N=4 superfield terms which preserve N=8 supersymmetry but break the superconformal and SO(7) symmetries.