Orbit method quantization of the AdS${}_2$ superparticle

Abstract

We consider the Hamiltonian reduction and canonical quantization of a massive AdS${}_2$ superparticle realized on the coset OSP(1|2)/SO(1,1). The phase space of the massive superparticle is represented as a coadjoint orbit of a timelike element of $\mathfrak{osp}$(1|2). This orbit has a well defined symplectic structure and the OSP(1|2) symmetry is realized as the Poisson bracket algebra of the Noether charges. We then construct canonical coordinates given by one bosonic and one fermionic oscillator, whose quantization leads to the Holstein-Primakoff type realization of $\mathfrak{osp}$(1|2). We also perform a similar analysis and discuss new features and inconsistencies in the massless case.

19 pages; v2: typos corrected, references added, matches published version

References in corpus (5)

• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• Konishi operator at intermediate coupling
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• Particle dynamics near extreme Kerr throat and supersymmetry
• On the Spectrum of the AdS_5xS^5 String at large lambda

Cited by in corpus (9)

• Towards a bulk description of higher spin SYK
• Superintegrability of Geodesic Motion on the Sausage Model
• General phase spaces: from discrete variables to rotor and continuum limits
• The S-matrix algebra of the AdS2 X S2 superstring
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Massless $Ad{S}_2$ scattering and Bethe ansatz
• Coset construction of AdS particle dynamics
• Quantization of the ${\mathrm{AdS}}_3$ Superparticle on $\mathrm{OSP}(1|2{)}^2/\mathrm{SL}(2,\mathbb{R})$
• On $OSp(N|2)$ superconformal mechanics