$\mathcal{N}=8$ supersymmetric mechanics with spin variables from indecomposable multiplets

Abstract

We define two new indecomposable (not fully reducible) $\mathcal{N}=8$, $d=1$ off-shell multiplets and consider the corresponding models of $\mathcal{N}=8$ supersymmetric mechanics with spin variables. Each multiplet is described off shell by a scalar superfield which is a nonlinear deformation of the standard scalar superfield $X$ carrying the $d=1$ multiplet $(1,8,7)$. Deformed systems involve, as invariant subsets, two different off-shell versions of the irreducible multiplet $(8,8,0)$. For both systems we present the manifestly $\mathcal{N}=8$ supersymmetric superfield constraints, as well as the component off- and on-shell invariant actions, which for one version exactly match those given in arXiv:2402.00539 [hep-th]. The two models differ off shell, but prove to be equivalent to each other on shell, with the spin variables sitting in the adjoint representation of the maximal $R$-symmetry group $\mathrm{SO}(8)$.

1+15 pages; v2: reference list corrected