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<inline-graphic></inline-graphic> 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<inline-graphic></inline-graphic>, 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<inline-graphic></inline-graphic>, in contrast to the BPS branch where c vanishes for all N≥2<inline-graphic></inline-graphic>. We briefly discuss potential repercussions this feature could have in a microscopic description of these black holes. [ABSTRACT FROM AUTHOR]