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.

arXiv comment10 pages, v2: additional remark in Conclusions, typos corrected, matches published version

References in corpus (8)

• Physics and Mathematics of Calogero particles
• Supersymmetric Calogero models by gauging
• (Super)conformal many-body quantum mechanics with extended supersymmetry
• $\mathcal{N}$-extended supersymmetric Calogero models
• Goldfish geodesics and Hamiltonian reduction of matrix dynamics
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• Gauged spinning models with deformed supersymmetry
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry

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