Abstract
We compute logarithmic corrections to the entropy of supersymmetric extremal
black holes in N=4 and N=8 supersymmetric string theories and find results in
perfect agreement with the microscopic results. In particular these logarithmic
corrections vanish for quarter BPS black holes in N=4 supersymmetric theories,
but has a finite coefficient for 1/8 BPS black holes in the N=8 supersymmetric
theory. On the macroscopic side these computations require evaluating the one
loop determinant of massless fields around the near horizon geometry, and
include, in particular, contributions from dynamical four dimensional gravitons
propagating in the loop. Thus our analysis provides a test of one loop quantum
gravity corrections to the black hole entropy, or equivalently of the
AdS\_2/CFT\_1 correspondence. We also extend our analysis to N=2 supersymmetric
STU model and make a prediction for the logarithmic correction to the black
hole entropy in that theory.
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