Abstract
We compute the statistical entropy of the three charge (D1-D5-p) five dimen- sional black hole to sub-leading order in a large charge expansion. We find an agreement with the macroscopic calculation of the Wald entropy in R 2 corrected supergravity theory. The two calculations have a overlapping regime of validity which is not the Cardy regime in the microscopic conformal field theory. We use this result to clarify the 4d-5d lift for black holes on Taub-NUT space. In particular, we compute sub-leading corrections to the formula S 4d = S 5d . In the microscopic analysis, this correction arises from excitations bound to the Taub-NUT space. In the macroscopic picture, the difference is accounted by a mechanism present in a higher derivative theory wherein the geometry of the Taub-NUT space absorbs some of the electric charge.
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