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.

arXiv comment15 pages

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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