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

TL;DR

This paper develops covariant worldline actions for various twistor particles in AdS spacetimes using coadjoint orbits, unifying different particle types including exotic ones through a twistorial framework.

Contribution

It introduces a universal twistorial formulation of worldline actions for particles in AdS, encompassing both standard and exotic particle species via coadjoint orbits.

Findings

Unified twistorial actions for massless, massive, and conformal particles.

Inclusion of exotic particles like tachyons and continuous spin particles.

Reproduction of known results for standard particles and extension to new particle types.

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.