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 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.

Black hole spectroscopy and AdS2 holography

“…The boundary modes listed for the KK block in we find a KK.bndy = 5 12 from (4.4). Adding the bulk contribution a KK.bulk = 1 72 , we get a KK.bulk+bndy = 31 72 , which also agrees with the result in [13].…”

“…With the bulk contribution a gravitino.bulk = − 17 1440 . Again, the sum a gravitino.bulk+bndy = − 137 1440 agrees with that of [13].…”

“…The entry for boundary modes a bndy includes naïve zero modes and a zero denotes the corrections determined by the more careful treatment. The sum a bulk +bndy is of interest since it can be compared with results from the local method [13]. We find agreement for each of the 5 type of blocks.…”

“…The 4D vector block couples a scalar field x and a gauge field through the Lagrangian [13] e −1 L vector = −…”

Seeley-DeWitt coefficients in $$ \mathcal{N} $$ = 2 Einstein-Maxwell supergravity theory and logarithmic corrections to $$ \mathcal{N} $$ = 2 extremal black hole entropy

“…These logarithmic corrections are universal in this sense that they appear in any generic theory of gravity. But c does not have the same sort of universality: it can be determined only from low energy modes, i.e., the spectrum of massless fields present in the theory, and are unconcerned about UV completion of the theory [3][4][5][6][7][8][9][10][11][12][13]. These correction terms are important as they provide us with the non-trivial information about the microstates of the black holes and hence providing a valuable testing ground for any candidate theory of quantum gravity.…”