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(Q1) × U(Q5) gauge theory. Finite horizon size at weak coupling requires both Q1 and Q5 to be large. We derive the result in the moduli space approximation (say for Q1 > Q5) and appeal to supersymmetry to argue its validity beyond weak coupling. As a result of a combination of quenched ZQ1 Wilson lines and a residual Weyl symmetry, the low-lying excitations of the U(Q1) × U(Q5) 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 RQ1Q5. We also discuss the appearance of a marginal perturbation of the effective conformal field theory for large but finite values of Q5.