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

Abstract

We compute the leading logarithmic correction to black hole entropy on the non-BPS branch of 4D $\mathcal{N}\ge 2$ 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 $\mathcal{N}=8,6,4,2$ supergravity, its spectrum of quadratic fluctuations in all these environments, and the resulting quantum corrections. We find that the $c$-anomaly vanishes only when $\mathcal{N}\ge 6$, in contrast to the BPS branch where $c$ vanishes for all $\mathcal{N}\ge 2$. We briefly discuss potential repercussions this feature could have in a microscopic description of these black holes.

41 pages, 8 tables. v2: minor typos corrected, the version published on JHEP