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Two faces of $N = 7$ , 8 superconformal mechanics

Sergey Krivonos ^1,2,* and Armen Nersessian ^1,3,4,†

¹Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia
²Laboratory of Applied Mathematics and Theoretical Physics, TUSUR, Lenina Avenue 40, 634050 Tomsk, Russia
³Yerevan Physics Institute, 2 Alikhanyan Brothers Street, Yerevan, 0036, Armenia
⁴Institute of Radiophysics and Electronics, Ashtarak-2, 0203, Armenia

^*Contact author: krivonos@theor.jinr.ru
^†Contact author: arnerses@yerphi.am

Phys. Rev. D 111, 125025 – Published 27 June, 2025

DOI: https://doi.org/10.1103/lp8v-7643

Abstract

Two variants of $N = 7$ superconformal mechanics with manifest $so (7)$ and $su (2) \times su (2)$ $R$ -symmetries possessing exceptional $G (3)$ dynamical symmetry are presented. To construct these $G (3)$ theories, we developed two new versions of covariant embedding of the exceptional $g_{2}$ algebra into the $so (7)$ algebra and then the embedding of $so (7)$ into $so (8)$ . As a result, two $N = 8$ superconformal mechanics with the $O S p (8 | 2)$ and $F (4)$ superconformal algebras and $N = 7, G (3)$ superconformal mechanics were constructed in a uniform way. The constants of the octonion multiplication play a key role in the construction of superconformal mechanics with manifest $so (7)$ symmetry.

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References (18)

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Phys. Rev. D 111, 125025– Published 27 June, 2025

Vol. 111, Iss. 12 — 15 June 2025

Received 5 May 2025
Accepted 10 June 2025

DOI: https://doi.org/10.1103/lp8v-7643

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Two faces of $N = 7$ , 8 superconformal mechanics

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Two faces of N=7, 8 superconformal mechanics

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Two faces of $N = 7$ , 8 superconformal mechanics