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$(8|2)$ symmetry, as well as OSp$(6|2)$-symmetric ones, by replacing the S$^7$ with the orbifold S$^7/\mathbb{Z}_k$. 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$_2\times \mathbb{CP}^3\times\text{S}^1\times I$ solutions by T-duality and establish a chain of dualities that maps the massless limit of these classes to AdS$_4/\mathbb{Z}_{k'}\times\text{S}^7/\mathbb{Z}_k$, thus identifying the brane configurations yielding these solutions. We propose that the ${\cal N}=8$ 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 ${\cal N}=6$ solutions.