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

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