Abstract
We construct a new off-shell $\mathcal{N}=8$, $d=1$ nonlinear supermultiplet $(\mathbf{4},\mathbf{8},\mathbf{4})$ proceeding from the nonlinear realization of the $\mathcal{N}=8$, $d=1$ superconformal group $OSp({4}^{\ensuremath{\star}}|4)$ in its supercoset $\frac{OSp({4}^{\ensuremath{\star}}|4)}{SU(2{)}_{\mathcal{R}}\ensuremath{\bigotimes}{D,K}\ensuremath{\bigotimes}SO(4)}$. The irreducibility constraints for the superfields automatically follow from appropriate covariant conditions on the $osp({4}^{\ensuremath{\star}}|4)$-valued Cartan superforms. We present the most general sigma-model type action for $(\mathbf{4},\mathbf{8},\mathbf{4})$ supermultiplet. The relations between linear and nonlinear $(\mathbf{4},\mathbf{8},\mathbf{4})$ supermultiplets and linear $\mathcal{N}=8$ $(\mathbf{5},\mathbf{8},\mathbf{3})$ vector supermultiplet are discussed.
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