Logarithmic Corrections to Entropy of Magnetically Charged AdS4 Black Holes

TL;DR

This work computes logarithmic corrections to the entropy of magnetically charged extremal AdS$_4$ black holes using the quantum entropy function in the AdS$_2$ near-horizon geometry, deriving a net quantum correction of $\Delta F = -12\ln a$ from one-loop massless fluctuations. By performing a detailed zero-mode analysis of bosonic and fermionic fields arising from 11d supergravity on $S^2\times S^7$, the authors decompose contributions into metric, form, ghost, and fermion sectors, confirming the final log term from both sectors. They outline potential routes to match this macroscopic result with the microscopic ABJM index, highlighting ensemble choices and large-$N$ vs large-$a$ scaling issues, including the presence or absence of an $N\ln N$ term. Overall, the paper provides a concrete IR quantum correction to the Wald entropy for AdS$_4$ black holes and maps out the steps necessary for a consistent microscopic comparison.

Abstract

We compute logarithmic corrections to the entropy of a magnetically charged extremal black hole in AdS4 x S7 using the quantum entropy function and discuss the possibility of matching against recently derived microscopic expressions.