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Dual 2d CFT Identification of Extremal Black Rings from Holes

Five dimensional Einstein gravity vacuum solutions in general fall into two classes of black rings with horizon topology S^2 \times S^1, and black holes with horizon topology S^3. These solutions are specified by their mass and two spins. There are "overlapping" regions of this parameter space where one has extremal rings and holes of the same spins. We show that for such regions the hole has generically a larger entropy than the ring, and likewise, the central charge of the proposed chiral 2d CFT dual to the hole is larger than that of the ring. For special places of this overlapping region where one of the spins tends to zero, the entropies of the extremal ring and hole also tend to zero and essentially become equal. In this case we are dealing with Extremal Vanishing Horizon (EVH) black holes or rings. The near horizon geometry of the near-EVH hole and rings both contain locally AdS_3 throats, providing a basis for the EVH/CFT proposal, a 2d CFT description of the low energy excitations of EVH hole or ring. We argue how the near-EVH hole and near-EVH ring can be distinguished from this dual 2d CFT viewpoint: The hole is a thermal state with zero temperature in the left sector and finite temperature in the right, while the ring is a generic state in the ground state (of the CFT on the plane) in the left sector and a thermal state in the right. The latter is part of the Hilbert space of the 2d CFT obtained in the Discrete Light Cone Quantization (DLCQ).