Higher spin algebras and large $\mathcal{N}=4$ holography

A new family of higher spin algebras that arises upon restricting matrix extensions of $\mathfrak{s}\mathfrak{h}\mathfrak{s}[\lambda ]$ is found. We identify coset CFTs realising these symmetry algebras, and thus propose new higher spin-CFT dual pairs. These higher spin theories arise naturally as a subsector of string theory on ${\mathrm{A}\mathrm{d}\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ for specific ratios of the radii of the two spheres.