Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

TL;DR

The paper shows that one-loop logarithmic corrections to extremal black hole entropy in ${\cal N}=2$ theories are governed by infrared data (massless spectra and couplings) and can be computed via the quantum entropy function in a near-horizon $AdS_2\times S^2$ geometry. It derives a universal formula for half-BPS black holes, $S_{BH}= {A_H\over 4G_N} + {1\over 12}(23+n_H-n_V)\ln {A_H\over G_N} + O(1)$, and provides explicit RN, pure ${\cal N}=2$, and matter-coupled results, including zero-mode treatments. The work tests OSV measure proposals, finding agreement with Denef–Moore in the weak coupling limit while highlighting non-local one-loop effects that challenge other proposals; it also discusses multi-centered contributions and ensemble choices. Overall, it connects infrared quantum corrections to macroscopic entropy, supports a constrained OSV framework, and clarifies the role of anomaly-inspired methods and zero modes in the entropy computation.

Abstract

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.