On ${\text{AdS}}_2\times {\text{S}}^7$, its ${\mathbb{Z}}_k$ orbifold and their dual quantum mechanics

We consider a previously constructed class of massive Type IIA AdS${}_2\times$S${}^7\times I$ solutions with OSp$(8\mathrm{\mid }2)$ symmetry, as well as OSp$(6\mathrm{\mid }2)$-symmetric ones, by replacing the S${}^7$ with the orbifold S${}^7\mathrm{/}{\mathbb{Z}}_k$. In both cases we construct global solutions for which the interval $I$ is bounded between physical singularities, by allowing D8-branes transverse to $I$. We also generate a new class of Type IIB AdS${}_2\times {\mathbb{C}\mathbb{P}}^3\times {\text{S}}^1\times I$ solutions by T-duality and establish a chain of dualities that maps the massless limit of these classes to AdS${}_4\mathrm{/}{\mathbb{Z}}_{k^{\mathrm{\prime }}}\times {\text{S}}^7\mathrm{/}{\mathbb{Z}}_k$, thus identifying the brane configurations yielding these solutions. We propose that the $\mathcal{N}=8$ solutions are dual to a theory living on a D0-F1-D8 brane intersection which has a description in terms of disconnected quivers and similarly for the $\mathcal{N}=6$ solutions.