Exact Counting of Supersymmetric Black Hole Microstates

It is shown that the entropy of certain two-charge supersymmetric black holes in $N=4$ string theories can be computed to all orders using Wald’s formula and the supersymmetric attractor equations with an effective action that includes the relevant higher curvature terms. Classically, these black holes have zero area but the attractor equations are still applicable at the quantum level and result in finite quantum area. The quantum corrected macroscopic entropy agrees precisely with the microscopic counting for an infinite tower of fundamental string states to all orders in an asymptotic expansion.