We study one-loop logarithmic corrections to the entropy of static hyperbolic BPS black holes in asymptotically AdS4 spacetime. Our analysis is carried out in a consistent real-scalar truncation of \( \mathcal{N} \) = 2 Fayet-Iliopoulos gauged supergravity specified by the prepotential F = –iX0X1, which corresponds to an Einstein-Dilaton-Maxwell theory with a nontrivial scalar potential. In this model, the classical BPS attractor mechanism exhibits flat directions, leaving scalar moduli on the black hole horizon unfixed, while the Bekenstein-Hawking entropy depends only on the charges. We show that the resulting one-loop correction to the black hole entropy acquires a nontrivial dependence on the horizon moduli and induces an effective quantum potential that dynamically stabilizes them at a preferred value. Our results provide an explicit and concrete realization of quantum lifting of classical attractor flat directions in gauged supergravity.
