Conformal invariance, N-extended supersymmetry and massless spinning particles in anti-de Sitter space

Starting with a manifestly conformal (O(d,2) invariant) mechanics model in d space and 2 time dimensions, we derive the action for a massless spinning particle in d-dimensional anti-de Sitter space. The action obtained possesses both gauge N-extended worldline supersymmetry and local O(N) invarince. Thus we improve the old statement by Howe et al. that the spinning particle model with extended worldline supersymmetry admits only flat space-time background for N > 2 (spin greater one). The original (d+2)-dimensional model is characterized by rather unusual property that the corresponding supersymmetry transformations do not commute with the conformal ones, in spite of the explicit O(d,2) invariance of the action