Abstract
Integrability of \(\mathcal{N}\) = 1 supersymmetric Ruijsenaars-Schneider three-body models based upon the potentials \(W\left(x\right)=\frac{2}{x}\), \(W\left(x\right)=\frac{2}{{\text{sin}}x}\), and \(W\left(x\right)=\frac{2}{{\text{sinh}}x}\) is proven. The problem of constructing an algebraically resolvable set of Grassmann-odd constants of motion is reduced to finding a triplet of vectors such that all their scalar products can be expressed in terms of the original bosonic first integrals. The supersymmetric generalizations are used to build novel integrable (iso)spin extensions of the respective Ruijsenaars-Schneider three-body systems.
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Acknowledgments
The author thanks T. Snegirev for the collaboration at an earlier stage of this project. This work is supported in part by RF Ministry of Science and Higher Education under the assignment FSWW-2023-0003.
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Galajinsky, A. Remarks on integrability of \(\mathcal{N}\) = 1 supersymmetric Ruijsenaars-Schneider three-body models. J. High Energ. Phys. 2024, 129 (2024). https://doi.org/10.1007/JHEP05(2024)129
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DOI: https://doi.org/10.1007/JHEP05(2024)129