Logarithmic corrections to black hole entropy: the non-BPS branch

Abstract

Abstract We compute the leading logarithmic correction to black hole entropy on the non-BPS branch of 4D N≥2 $$ \mathcal{N}\ge 2 $$ 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 N=8 $$ \mathcal{N}=8 $$, 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 N≥6 $$ \mathcal{N}\ge 6 $$, in contrast to the BPS branch where c vanishes for all N≥2 $$ \mathcal{N}\ge 2 $$. We briefly discuss potential repercussions this feature could have in a microscopic description of these black holes.

Keywords

• Black Holes in String Theory
• Extended Supersymmetry