Logarithmic Corrections to Black Hole Entropy: the Non-BPS Branch

TL;DR

The paper addresses whether logarithmic quantum corrections to black hole entropy on the non-BPS branch are universal. By embedding a minimal Kaluza-Klein black hole into ${\cal N}=8,6,4,2$ supergravity and analyzing quadratic fluctuations with heat-kernel methods, it extracts Seeley-DeWitt coefficients and the resulting $c$- and $a$-anomalies that control the log term. A key result is that the $c$-anomaly vanishes for ${\cal N}\geq 6$ on the non-BPS branch, yielding universal log corrections, while $c\neq 0$ for ${\cal N}=2,4$, making the log dependent on black hole parameters; explicit non-extremal and extremal corrections are provided. The work uses consistent truncations and direct ${\cal N}=2$ analyses to map fluctuation spectra, suggesting deep links between high supersymmetry and microscopic descriptions of black hole microstates. It opens avenues for refining microscopic accounts of non-BPS black holes and for exploring more general backgrounds with nontrivial dilatons or rotations.

Abstract

We compute the leading logarithmic correction to black hole entropy on the non-BPS branch of 4D ${\cal N}\geq 2$ supergravity theories. This branch corresponds to finite temperature black holes whose extremal limit does not preserve supersymmetry, such as the $D0-D6$ system in string theory. Starting from a black hole in minimal Kaluza-Klein theory, we discuss in detail its embedding into ${\cal N}=8, 6, 4, 2$ supergravity, its spectrum of quadratic fluctuations in all these environments, and the resulting quantum corrections. We find that the $c$-anomaly vanishes only when ${\cal N}\geq 6$, in contrast to the BPS branch where $c$ vanishes for all ${\cal N}\geq 2$. We briefly discuss potential repercussions this feature could have in a microscopic description of these black holes.