We compute the supersymmetric entropy of the most general BPS black hole in 4d N=2 supergravity coupled to nV vector multiplets, obtained from Type IIA string theory compactified on a Calabi--Yau threefold at large volume, including the all-genera leading-order '-corrections. These can be equivalently seen as D0-brane quantum effects from a dual five-dimensional M-theory perspective. We find that these corrections generically lead to both perturbative and non-perturbative contributions to the black hole entropy. We argue that the exception occurs for certain specific configurations where the gauge background, seen through the lens of D0-brane probes, behaves as purely electric or purely magnetic, thereby accounting for the absence of such non-perturbative effects. To explore this further, we perform a semiclassical analysis of the (non-) BPS particle dynamics in the near-horizon geometry of the underlying black hole, which is described by a maximally supersymmetric AdS₂ S² solution. As a byproduct, this study provides additional insights into the non-perturbative stability of supersymmetric black hole geometries and suggests an interpretation in terms of complex saddles contributing to the worldline path integral.
Alberto Castellano, Dieter Lüst, Carmine Montella, Matteo Zatti (Fri,) studied this question.