Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part II: Twistorial Descriptions

Abstract

Worldline actions for various twistor particles in AdS spacetimes are constructed from the coadjoint orbits of $Sp(4,\mathbb R)$, $SU(2,2)$ and $O^*(8)$ as constrained Hamiltonian systems. The constraints are associated with the coadjoint orbits of the dual groups, respectively identified as $O(p,M-p)$, $U(p, M-p)$ and $Sp(p, M-p)$. These actions are presented in a universal form by making use of the twistor variables taking value in $\mathbb R$, $\mathbb C$ and $\mathbb H$, respectively. We find that the massless, massive and the conformal particles (namely the singletons) of any spins appear for the compact dual groups with $p=0$ reproducing many of the results in earlier literature, whereas more exotic particle species, such as various tachyons, continuous spin particles and BdS particles appear for the non-compact dual groups.