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

TL;DR

This paper calculates the leading logarithmic quantum correction to the entropy of non-BPS black holes in 4D supergravity, revealing how supersymmetry level affects the anomaly and implications for microscopic models.

Contribution

It provides a detailed computation of quantum corrections for non-BPS black holes across various supergravity theories, highlighting the role of supersymmetry in anomaly cancellation.

Findings

The c-anomaly vanishes only for ${ m N} extgreater=6$ supergravity.

Quantum corrections depend on the supersymmetry level of the theory.

Differences between BPS and non-BPS branches in anomaly behavior.

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.