Carmine Montella (MPI - Monaco)

From Black holes to the Swampland and back

In this talk, we investigate the supersymmetric entropy of four-dimensional N=2 BPS black holes obtained as solutions of Type IIA string theory compactified on a Calabi–Yau threefold. To uncover its non-perturbative structure, we perform the full path integral for an N=2 hypermultiplet in the near-horizon region, AdS₂ × S². We prove that this computation admits a natural interpretation as the analogue of the Gopakumar–Vafa formula realized directly in the attractor geometry. In the large-volume regime, we derive the quantum entropy of the most general solution, incorporating all-genus leading-order α′-prime corrections. We then extend these tools to compute non-perturbative effects in extremal black holes induced by super-extremal particles, obtaining a sharp bound that signals instabilities. Finally, we discuss the connection with the Weak Gravity Conjecture.