Higher Spins from Nonlinear Realizations of $OSp(1\mathrm{\mid }8)$

We exhibit surprising relations between higher spin theory and nonlinear realizations of the supergroup $OSp(1\mathrm{\mid }8)$, a minimal superconformal extension of N=1, 4D supersymmetry with tensorial charges. We construct a realization of $OSp(1\mathrm{\mid }8)$ on the coset supermanifold $OSp(1\mathrm{\mid }8)\mathrm{/}SL(4,R)$ which involves the tensorial superspace $R^{(10\mathrm{\mid }4)}$ and Goldstone superfields given on it. The covariant superfield equation encompassing the component ones for all integer and half-integer massless higher spins amounts to the vanishing of covariant spinor derivatives of the suitable Goldstone superfields, and, via Maurer-Cartan equations, to the vanishing of $SL(4,R)$ supercurvature in odd directions of $R^{(10\mathrm{\mid }4)}$. Aiming at higher spin extension of the Ogievetsky-Sokatchev formulation of N=1 supergravity, we generalize the notion of N=1 chirality and construct first examples of invariant superfield actions involving a non-trivial interaction. Some other potential implications of $OSp(1\mathrm{\mid }8)$ in the proposed setting are briefly outlined.