Supersymmetric extensions of oscillator- and Coulomb-like systems

Abstract

We suggest the 𝑠𝑢(1, 𝑁|𝑀)-superconformal mechanics formulated in terms of phase superspace given by the non-compact analog of complex projective superspace CP𝑁|𝑀. We parameterized this phase space by the specific coordinates allowing us to interpret it as a higher-dimensional super-analog of the Lobachevsky plane parameterized by lower half-plane (Klein model). Then we transited to 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 the proposed scheme allows constructing the 𝑠𝑢(1, 𝑁|𝑀) superconformal extensions of a wide class of superintegrable systems. We also proposed the superintegrable oscillator-like system with a 𝑠𝑢(1, 𝑁|𝑀) dynamical superalgebra, and found that it admits deformed N = 2𝑀 Poincaré supersymmetry.