Hierarchy of N=8 Mechanics Models

Understand

Using the N=4 superspace approach in one dimension (time), we construct general N=8 supersymmetric mechanics actions for the multiplets (b,8,8-b) classified in hep-th/0406015, with the main focus on the previously unexplored cases of (8,8,0), (7,8,1) and (6,8,2), as well as on (5,8,3) for completeness.

• N=8 supersymmetry of the action amounts to a harmonicity condition for the Lagrangian with respect to its superfield arguments.
• We derive the generic off-shell component action for the ``root'' multiplet (8,8,0), prove that the actions for all other multiplets follow from it through automorphic dualities and argue that this hierarchical structure is universal.
• The bosonic target geometry in all cases is conformally flat, with a unique scalar potential (except for the root multiplet).