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Logarithmic corrections to the extremal black hole entropy can be computedpurely in terms of the low energy data -- the spectrum of massless fields andtheir interaction. The demand of reproducing these corrections provides astrong constraint on any microscopic theory of quantum gravity that attempts toexplain the black hole entropy. Using quantum entropy function formalism wecompute logarithmic corrections to the entropy of half BPS black holes in N=2supersymmetric string theories. Our results allow us to test various proposalsfor the measure in the OSV formula, and we find agreement with the measureproposed by Denef and Moore if we assume their result to be valid at weaktopological string coupling. Our analysis also gives the logarithmiccorrections to the entropy of extremal Reissner-Nordstrom black holes inordinary Einstein-Maxwell theory.

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates