Abstract:
We consider reducible but indecomposable multiplets of $\mathcal N = 4$ and $\mathcal N = 8$ supersymmetric mechanics. The indecomposable $\mathcal N = 4$ multiplet is described by an unconstrained scalar superfield that corresponds to the multiplet $(1,4,3)$ linearly coupled to the irreducible multiplet $(3,4,1)$. Employing the superfield approach, we construct a coupled system with spin variables, and show that the corresponding on-shell Lagrangian reproduces the model of Fedoruk–Ivanov–Lechtenfeld (2012). In case of $\mathcal N = 8$ supersymmetry, we consider two indecomposable multiplets as two different deformations of the scalar superfield describing the multiplet $(1,8,7)$ non-linearly coupled to two different versions of the irreducible multiplet $(8,8,0)$. We construct invariant Lagrangians with spin variables for both multiplets at the component level. We show that one of them coincides with the model of Fedoruk–Ivanov (2024) constructed in terms of $\mathcal N = 4$ superfields. Based on:
E. Ivanov, S. Sidorov, Phys. Rev. D 93 (2016) 065052, arXiv:1509.05561 [hep-th].S. Sidorov, J. Phys. A 58 (2025) 025210, arXiv:2410.11618 [hep-th].E. Ivanov, S. Sidorov, in progress.
