Towards a derivation of holographic entanglement entropy. (English) Zbl 1296.81073
Summary: We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry. Hence the conformal transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. The AdS/CFT dictionary allows us to calculate this thermodynamic entropy as the horizon entropy of a certain topological black hole. In even dimensions, we also demonstrate that the universal contribution to the entanglement entropy is given by \(A\)-type trace anomaly for any CFT, without reference to holography.
MSC:
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 94A17 | Measures of information, entropy |
| 82B30 | Statistical thermodynamics |
| 83C57 | Black holes |
| 83F05 | Relativistic cosmology |
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