Quantization of the AdS3 superparticle on OSP(1|2)2/SL(2,R)

Abstract

We analyze AdS3 superparticle dynamics on the coset OSP(1|2)×OSP(1|2)/SL(2,R). The system is quantized in canonical coordinates obtained by gauge invariant Hamiltonian reduction. The left and right Noether charges of a massive particle are parametrized by coadjoint orbits of a timelike element of osp(1|2). Each chiral sector is described by two bosonic and two fermionic canonical coordinates corresponding to a superparticle with superpotential W=q−m/q, where m is the particle mass. Canonical quantization then provides a quantum realization of osp(1|2)⊕osp(1|2). For the massless particle the chiral charges lie on the coadjoint orbit of a nilpotent element of osp(1|2) and each of them depends only on one real fermion, which demonstrates the underlying κ-symmetry. These remaining left and right fermionic variables form a canonical pair and the system is described by four bosonic and two fermionic canonical coordinates. Due to conformal invariance of the massless particle, the osp(1|2)⊕osp(1|2) extends to the corresponding superconformal algebra osp(2|4). Its 19 charges are given by all real quadratic combinations of the canonical coordinates, which trivializes their quantization.