Exact Counting of Black Hole Microstates

The exact entropy of two-charge supersymmetric black holes in N=4 string theories is 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. 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.