科研之友
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摘要
Using a holographic proposal for the geometric entropy we study its behavior in the geometry of Schwarzschild black holes in global AdS(p) for p = 3, 4, 5. Holographically, the entropy is determined by a minimal surface. On the gravity side, due to the presence of a horizon on the background, generically there are two solutions to the surfaces determining the entanglement entropy. In the case of AdS(3), the calculation reproduces precisely the geometric entropy of an interval of length l in a two-dimensional conformal field theory with periodic boundary conditions. We demonstrate that in the cases of AdS(4) and AdS(5) the sign of the difference of the geometric entropies changes, signaling a transition. Euclideanization implies that various embedding of the holographic surface are possible. We study some of them and find that the transitions are ubiquitous. In particular, our analysis renders a very intricate phase space, showing, for some ranges of the temperature, up to three branches. We observe a remarkable universality in the type of results we obtain from AdS(4) and AdS(5).
- 出版日期2012-4-10
