Moduli-dependent one-loop entropy of hyperbolic BPS black hole in AdS4

A bstract We study one-loop logarithmic corrections to the entropy of static hyperbolic BPS black holes in asymptotically AdS 4 spacetime. Our analysis is carried out in a consistent real-scalar truncation of $$ \mathcal{N} $$ N = 2 Fayet-Iliopoulos gauged supergravity specified by the prepotential F = – iX 0 X 1 , 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.