K\'ahler geometry for $su(1,N|M)$-superconformal mechanics
| Autor: | Khastyan, Erik, Krivonos, Sergey, Nersessian, Armen |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Phys. Rev. A ,105, 025007(2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.105.025007 |
| Popis: | 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 $\mathcal{N}=2M$ Poincar\'e supersymmetry, in contrast with Coulomb-like ones. Comment: 15 pages |
| Databáze: | arXiv |
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