Conformal Invariance, N-extended Supersymmetry and Massless Spinning Particles in Anti-de Sitter Space
Abstract
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.