Kähler geometry for $su(1,N|M)$-superconformal mechanics

Abstract

We suggest the $su(1,N|M)$-superconformal mechanics formulated in terms of phase superspace given by the non-compact analogue of complex projective superspace ${\mathbb{CP}}^{N|M}$. We parameterized this phase space by the specific coordinates allowing to interpret it as a higher-dimensional super-analogue of the Lobachevsky plane parameterized by lower half-plane (Klein model). Then we introduced the canonical coordinates corresponding to the known separation of the "radial" and "angular" parts of (super)conformal mechanics. Relating the "angular" coordinates with action-angle variables we demonstrated that proposed scheme allows to construct the $su(1,N|M)$ supeconformal extensions of wide class of superintegrable systems. We also proposed the superintegrable oscillator- and Coulomb- like systems with a $su(1,N|M)$ dynamical superalgebra, and found that oscillator-like systems admit deformed $\mathcal{N}=2M$ Poincaré supersymmetry, in contrast with Coulomb-like ones.

15 pages

References in corpus (8)

• Action-angle variables for dihedral systems on the circle
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Lobachevsky geometry of (super)conformal mechanics
• The Tremblay-Turbiner-Winternitz system on spherical and hyperbolic spaces : Superintegrability, curvature-dependent formalism and complex factorization
• SU(2|2) supersymmetric mechanics
• Near-horizon dynamics of particle in extreme Reissner-Nordström and Clément-Gal'tsov black hole backgrounds: action-angle variables
• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
• Symmetries of deformed supersymmetric mechanics on Kähler manifolds

Cited by in corpus (3)

• The geometry of gauged (super)conformal mechanics
• Euler top and freedom in supersymmetrization of one-dimensional mechanics
• Weak supersymmetric $su(N|1)$ quantum systems