Superconformal mechanics from N-extended Euler-Calogero-Moser and Calogero models
arXiv:2607.11468
The paper constructs two‑particle superconformal mechanical models by decoupling the center of mass in N‑extended Euler‑Calogero‑Moser and Calogero systems, revealing SU(1,1|N) symmetry for the former and Osp(N|2) symmetry for the latter, and shows how spin variables can be incorporated.
Abstract
In this paper, we considered two-particle variants of the N-extended Euler-Calogero-Moser and Calogero models. Due the translation invariance, the center of mass can be decoupled (together with the corresponding fermions), leaving us with specific superconformal mechanics. Additional bosonic variables (spin variables) can easily be incorporated into the supercharges and the Hamiltonian. In the case of the Euler-Calogero-Moser model, the supersymmetry in the two-particle cases admits an unexpected extension from Osp(N|2) to SU(1,1|N) superconformal symmetry. The case of the Calogero model leads to purely Osp(N|2) superconformal mechanics. The way to get rid of the well-known problems along this path is to have a higher number of fermions present in the system.
11 pages, references corrected