Abstract
\(\mathcal{N}\) = 2 and \(\mathcal{N}\) = 4 supersymmetric generalizations of the 3-particle elliptic Calogero system are proposed. Supersymmetry generators of the system are found in which the center of mass sector is described by the supermultiplet \(({\mathbf{1}},\mathcal{N},\mathcal{N} - {\mathbf{1}})\), while the sector of relative coordinates is the supermultiplet \(({\mathbf{2}},\mathcal{N},\mathcal{N} - {\mathbf{2}})\). The \(\mathcal{N}\) = 2 model with three supermultiplets \(({\mathbf{1}},{\mathbf{2}},{\mathbf{1}})\) is also presented.
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Notes
The 2-particle Calogero system reduces to separated one-dimensional subsystems of the center of mass and relative motion, and supersymmetrization of each of them does not cause difficulties.
For brevity, the \({{q}_{a}} - {{q}_{b}}\) variables will be called below relative or difference coordinates, and the dynamic sector described by such coordinates will be called the relative sector of the system.
The application of the system obtained in [14] to describe the \(\mathcal{N}\) = 2 elliptic Calogero system was not discussed, although this is possible within the framework of the approach considered there.
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ACKNOWLEDGMENTS
I would like to thank Evgeny Ivanov and Sergey Krivonos for useful discussions and comments.
Funding
This work was supported by the Russian Science Foundation grant no. 21-12-00129.
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Fedoruk, S.A. Supersymmetrization of the 3-Particle Elliptic Calogero Model. Phys. Part. Nuclei Lett. 20, 560–564 (2023). https://doi.org/10.1134/S154747712304026X
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DOI: https://doi.org/10.1134/S154747712304026X