New variants of N = 3, 4 superconformal mechanics
Новые варианты N = 3, 4 суперсимметричных механик

Additional data

Submitted: 30.10.2025; Accepted: 19.12.2025; Published 26.12.2025;
Views: 101; Downloaded: 42

How to Cite

N. Kozyrev, S. Krivonos. "New variants of N = 3, 4 superconformal mechanics" Natural Sci. Rev. 2 100505 (2025)
https://doi.org/10.54546/NaturalSciRev.100505
BibTex
N. Kozyrev1,a, S. Krivonos1,2,b
  • 1Joint Institute for Nuclear Research, 141980 Dubna, Russia
  • 2Tomsk State University of Control Systems and Radioelectronics (TUSUR), Lenin Ave. 40, 634050 Tomsk, Russia
  • ankozyrev@theor.jinr.ru
  • bkrivonos@theor.jinr.ru
DOI: 10.54546/NaturalSciRev.100505
Keywords: superconformal mechanics, N-extended supersymmetry, integrable system, Schwarzians
Topics: Physics , High Energy Physics (Theory) , Mathematical physics
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Abstract

We construct superconformal mechanics with N = 3 and N = 4 supersymmetries that were inspired by analogy with the supersymmetric Schwarzian mechanics. The Schwarzian, being another system with superconformal symmetry, provides insight into the field content of supersymmetric mechanics, most notably, on the number and properties of the fermionic fields involved. Adding more fermionic fields (four in the N = 3 case and eight in the N = 4 case) made it possible to construct systems possessing maximal superconformal symmetries in N = 3 and N = 4, namely osp(3|2) and D(1, 2; α). In the case of N = 4 supersymmetry, we explicitly construct a new variant of N = 4 superconformal mechanics in which all bosonic subalgebras of the D(1, 2; α) superalgebra have a bosonic realization. In addition, the constructed systems involve the so(3) currents whose parameterization is not fixed, which allows one to consider different underlying geometries.

Acknowledgements

We thank Armen Nersessian for useful discussions on the subject of this paper. SK acknowledges partial financial support of the Ministry of Science and Higher Education of the Russian Federation, Government Order for 2023–2025, Project No. FEWM-2023-0015 (TUSUR).

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