Regular 3-charge 4D black holes and their microscopic description

The perturbative ${\alpha }^{\mathrm{\prime }}$ corrections to Type-IIA String Theory compactified on a Calabi-Yau three-fold allow the construction of regular three-charge supersymmetric black holes in four dimensions, whose entropy scales with the charges as $S\sim {\left(p^1{p}^2{p}^3\right)}^{\frac{2}{3}}$. We construct an M-theory uplift of these quantum black holes and show that they can be interpreted as arising from three stacks of M2 branes on a conical singularity. This in turns allow us relate them via a series of dualities to a system of D3 branes carrying momentum and thus to give a microscopic interpretation of their entropy.