D-brane Black Holes: Large-N Limit and the Effective String Description

We address the derivation of the effective conformal field theory description of the 5-dimensional black hole, modelled by a collection of D1- and D5- branes, from the corresponding low energy U(Q_1)xU(Q_5) gauge theory. Finite horizon size at weak coupling requires both Q_1 and Q_5 to be large. We derive the result in the moduli space approximation and appeal to supersymmetry to argue its validity beyond weak coupling. As a result of a combination of Z_{Q_1} Wilson lines and a residual Weyl symmetry, the low-lying excitations of the U(Q_1)xU(Q_5) gauge theory are described by an effective N=4 superconformal field theory with c=6 in 1+1 dimensions, where the space is a circle of radius RQ_1Q_5.