The phase diagram of the D1-D5 CFT and localized black holes
In this paper we analyze the phases that dominate the microcanonical ensemble at various energies in the D1-D5 CFT, which is dual to type II string theory on $AdS_3 \times S^3\times T^4$. We focus on black hole solutions, and on the dependence of the phase structure on the ratio of the size of the torus to the AdS scale; as small localized black holes (with horizon topology $S^8$) grow, they can start to fill the $S^3$ or the $T^4$ or both, and we analyze the general aspects of the transitions between the various phases of uniform and non-uniform black holes, incorporating known solutions and discussing the properties of additional unknown solutions. Some features of the transitions between these phases are similar to higher dimensional AdS spaces, while other features are different. We provide evidence that when the torus is much larger than the AdS radius, there is a large range of energies where the typical states are a novel phase, described by a lattice (in the $T^4$ directions) of black holes with horizon topology $S^5\times S^3$. In this phase the entropy is linear in the energy, with a coefficient that is of order the AdS radius.