Moduli-dependent one-loop entropy of hyperbolic BPS black hole in AdS$_4$

TL;DR

The paper computes one-loop logarithmic corrections to the entropy of static hyperbolic BPS black holes in AdS$_4$ within a Fayet–Iliopoulos gauged ${ m N}=2$ supergravity truncation to Einstein–Dilaton–Maxwell theory. Using heat-kernel methods, it separates local Seeley–DeWitt contributions and global zero-mode effects, revealing a nontrivial horizon-modulus ($\nu$) dependence that generates an effective quantum potential stabilizing the unfixed moduli. The results demonstrate quantum lifting of classical attractor flat directions in gauged supergravity and provide consistency checks by reducing to EDM, minimal gauged supergravity, and pure gravity, yielding model-specific but structurally similar logarithmic corrections. The findings highlight non-topological, moduli-dependent corrections in AdS settings and point toward future work on the fully supersymmetric theory and the integration measure over horizon moduli. $${\cal S}_{\rm QEF}={\cal S}_{\rm BH}^{\rm class.}+C\ln\frac{A_H}{G_N}+\cdots,$$ with $C$ receiving both local and global contributions that depend on horizon data such as $\nu$ and the AdS$_2$–horizon volume.

Abstract

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 ${\cal N}=2$ Fayet-Iliopoulos gauged supergravity specified by the prepotential $F=-i X^0 X^1$, 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.