Multi-Centered Black Hole Index from a Superconformal Quiver Index

We formulate a $D(2,1;0)$ superconformal index for scaling quiver quantum mechanics in its gauged sigma model description. These quivers describe the Coulomb-branch dynamics of multi-centered D-brane configurations in the $Ad{S}_2$ scaling limit of type II Calabi–Yau compactifications. Using supersymmetric localization, we obtain a fixed-point formula for this superconformal quiver index which reproduces the Manschot–Pioline–Sen index $g_{\mathrm{r}\mathrm{e}\mathrm{f}}$ of multi-centered BPS black hole solutions.