A simple particle action from a twistor parametrization of AdS5

The SO(4,2) isometries of AdS5 are realized non-linearly on its horospherical coordinates (xm,ρ). On the other hand, Penrose twistors have long been known to linearly realize these symmetries on 4-dimensional Minkowski space, the boundary of AdS5, parametrized by xm. Here we extend the twistor construction and define a pair of twistors, allowing us to include a radial coordinate in the construction. The linear action of SO(4,2) on the twistors induces the correct isometries of AdS5. We apply this new construction to the study of the dynamics of a massive particle in AdS5. We show that in terms of the twistor variables the action takes a simple form of a 1-dimensional gauge theory. Our result might open up the possibility to find a simple worldvolume action also for the string propagating on AdS5.