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

TL;DR

This paper calculates one-loop quantum corrections to the entropy of hyperbolic BPS black holes in AdS4, revealing how quantum effects stabilize scalar moduli that are classically unfixed.

Contribution

It demonstrates the quantum lifting of classical flat directions in the attractor mechanism of gauged supergravity black holes.

Findings

One-loop corrections depend on horizon moduli.

Quantum effects stabilize scalar moduli.

Explicit realization of quantum attractor lifting.

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.