One-Loop Test of Quantum Black Holes in anti–de Sitter Space

Abstract

Within 11-dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS_{4} black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.