Supersymmetric many-body Euler-Calogero-Moser model

Abstract

We explicitly construct a supersymmetric $so(n)$ spin-Calogero model with an arbitrary even number $\mathcal{N}$ of supersymmetries. It features $\frac{1}{2}\mathcal{N}n(n+1)$ rather than $\mathcal{N}n$ fermionic coordinates and a very simple structure of the supercharges and the Hamiltonian. The latter, together with additional conserved currents, form an $osp(\mathcal{N}|2)$ superalgebra. We provide a superspace description for the simplest case, namely $\mathcal{N}=2$ supersymmetry. The reduction to an $\mathcal{N}$-extended supersymmetric goldfish model is also discussed.

10 pages, v2: additional remark in Conclusions, typos corrected, matches published version

References in corpus (4)

• Physics and Mathematics of Calogero particles
• Supersymmetric Calogero models by gauging
• Goldfish geodesics and Hamiltonian reduction of matrix dynamics
• Gauged spinning models with deformed supersymmetry

Cited by in corpus (7)

• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Fifth-order generalized Heisenberg supermagnetic models
• Superfield approach to higher derivative N=1 superconformal mechanics
• N=2 supersymmetric extensions of relativistic Toda lattice
• $\mathcal{N}=4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model
• Spinning particles on 2-sphere in accord with the Bianchi classification
• Integrability of supersymmetric Calogero-Moser models