D-Branes in ${\mathbf{\text{AdS}}}_3\times {\mathbf{\text{S}}}^3\times {\mathbf{\text{S}}}^3\times {\mathbf{\text{S}}}^1$

String theory on ${\mathrm{A}\mathrm{d}\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ with two units of NS flux through each of the two $3$-spheres (and one unit of NS flux supporting the ${\mathrm{A}\mathrm{d}\mathrm{S}}_3$ factor) was recently argued to be exactly dual to the symmetric orbifold of eight free fermions and two bosons. This setup is interesting since it allows for a simple NS-R description. In this paper we study the spherical D-branes of this theory, and identify them with branes in the dual symmetric orbifold theory. We also comment briefly on the ${\mathrm{A}\mathrm{d}\mathrm{S}}_2$ branes.