AdS/CFT duals of topological black holes and the entropy of zero-energy states

The horizon of a static black hole in anti-de Sitter space can be spherical , planar, or hyperbolic. The microscopic dynamics of the first two classes of black holes have been extensively discussed recently within the context of the AdS/CFT correspondence. We argue that hyperbolic black holes introdu ce new and fruitful features in this respect, allowing for more detailed co mparisons between the weak and strong coupling regimes. In particular, by f ocussing on the stress tensor and entropy of some particular states, we ide ntify unexpected increases in the entropy of Super-Yang-Mills theory at str ong coupling that are not accompanied by increases in the energy. We descri be a highly degenerate state at zero temperature and zero energy density. W e also find that the entanglement entropy across a Rindler horizon in exact AdS(5) is larger than might have been expected from the dual SYM theory. B esides, we show that hyperbolic black holes can be described as thermal Rin dler states of the dual conformal field theory in at space.