${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry

Abstract

We propose new superintegrable mechanical system on the complex projective space ${\mathbb{CP}}^N$ involving a potential term together with coupling to a constant magnetic fields. This system can be viewed as a ${\mathbb{CP}}^N$-analog of both the flat singular oscillator and its spherical analog known as "Rosochatius system". We find its constants of motion and calculate their (highly nonlinear) algebra. We also present its classical and quantum solutions. The system belongs to the class of "Kähler oscillators" admitting $SU(2|1)$ supersymmetric extension. We show that, in the absence of magnetic field and with the special choice of the characteristic parameters, one can construct $\mathcal{N}=4,d=1$ Poinacaré supersymmetric extension of the system considered.

arXiv comment14 pages, minor improvements, misprints corrected, one reference added

References in corpus (35)

• Rigid Supersymmetric Theories in Curved Superspace
• Quantum Hall Effect in Higher Dimensions
• Exploring Curved Superspace
• Path Integral Discussion for Smorodinsky-Winternitz Potentials: I.\ Two- and Three Dimensional Euclidean Space
• (Super)Oscillator on CP(N) and Constant Magnetic Field
• Neumann-Rosochatius integrable system for strings on AdS_4 x CP^3
• Weak supersymmetry
• A note on N=4 supersymmetric mechanics on Kähler manifolds
• Deformed Supersymmetric Mechanics
• Superintegrable models related to near horizon extremal Myers-Perry black hole in arbitrary dimension
• SQM with Non-Abelian Self-Dual Fields: Harmonic Superspace Description
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Super Kähler oscillator from SU(2|1) superspace
• Superconformal mechanics in SU(2|1) superspace
• Quantum Oscillator on $\DC P^n$ in a constant magnetic field
• Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Self-duality and supersymmetry
• Spinning strings in the $\eta$-deformed Neumann-Rosochatius system
• Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere
• Integrability of the eta-deformed Neumann-Rosochatius model
• SU(2|2) supersymmetric mechanics
• Spherical Calogero model with oscillator/Coulomb potential: quantum case
• Klein-Gordonization: mapping superintegrable quantum mechanics to resonant spacetimes
• ${\mathbb{C}}^N$-Smorodinsky-Winternitz system in a constant magnetic field
• Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems
• Near horizon extremal Myers-Perry black holes and integrability of associated conformal mechanics
• Spherical Calogero model with oscillator/Coulomb potential: classical case
• On integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions
• $\mathcal{N}=4$ supersymmetric mechanics on curved spaces
• SU(2$|$1) supersymmetric mechanics on curved spaces
• Deformed $\mathcal{N}=8$ mechanics of $(8,8,0)$ multiplets
• Isospin particle systems on quaternionic projective spaces
• Superintegrable systems, polynomial algebra structures and exact derivations of spectra
• Quaternion-Kähler N=4 Supersymmetric Mechanics

Cited by in corpus (7)

• Cylindrical type integrable classical systems in a magnetic field
• $N$-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra $\mathcal{S}\mathcal{W}(N)$
• Symmetries of deformed supersymmetric mechanics on Kähler manifolds
• SU$(2|1)$ supersymmetric spinning models of chiral superfields
• Quantum SU$(2|1)$ supersymmetric ${\mathbb{C}}^N$ Smorodinsky--Winternitz system
• Generalized MICZ-Kepler systems on three-dimensional sphere and hyperboloid
• Superintegrable deformations of oscillator and Coulomb systems