Quantization of the ${\mathrm{AdS}}_3$ Superparticle on $\mathrm{OSP}(1|2{)}^2/\mathrm{SL}(2,\mathbb{R})$

Abstract

We analyze ${\mathrm{AdS}}_3$ superparticle dynamics on the coset $\mathrm{OSP}(1|2)\times \mathrm{OSP}(1|2)/\mathrm{SL}(2,\mathbb{R})$. 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 $\mathfrak{osp}(1|2)$. 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 $\mathfrak{osp}(1|2)\oplus \mathfrak{osp}(1|2)$. For the massless particle the chiral charges lie on the coadjoint orbit of a nilpotent element of $\mathfrak{osp}(1|2)$ and each of them depends only on one real fermion, which demonstrates the underlying $\kappa$-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 $\mathfrak{osp}(1|2)\oplus \mathfrak{osp}(1|2)$ extends to the corresponding superconformal algebra $\mathfrak{osp}(2|4)$. Its 19 charges are given by all real quadratic combinations of the canonical coordinates, which trivializes their quantization.

arXiv comment25+1 pages; v2: minor changes, references added and updated; v3: minor changes, one reference added, matches published version

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