Abstract
We review recent progress in understanding the entanglement entropy of gravitational configurations for anti-de Sitter gravity in two and three spacetime dimensions using the AdS/CFT correspondence. We derive simple expressions for the entanglement entropy of two- and three-dimensional black holes. In both cases, the leading term of the entanglement entropy in the large black hole mass expansion reproduces exactly the Bekenstein-Hawking entropy, whereas the subleading term behaves logarithmically. In particular, for the BTZ black hole the leading term of the entanglement entropy can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus.
Highlights
Entanglement is one of the most basic features of quantum mechanics
There are several arguments indicating that our derivation of the entanglement entropy (EE) of 2D AdS black holes could be extended to black holes in 3D AdS spacetime, i.e. to the BTZ black hole
We will show that the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, and in particular the UV/IR relation, allows us to identify in a natural way β and γ in terms of the two fundamental bulk length-scales, the horizon of the BTZ black hole r+ and the AdS length
Summary
Entanglement is one of the most basic features of quantum mechanics. Historically, it has generated a long debate about the nondeterministic character of quantum mechanics. A quantum state in a black hole geometry is divided by the horizon into two disconnected parts, and an external observer has to trace over the part of the state in the black hole interior Another strong hint pointing to a fundamental relationship between entanglement and Bekenstein-Hawking (BH) entropy is that both quantities scale as the area of the boundary. The usual statistical interpretation of the BH entropy—aiming to explain the black hole entropy in terms of microstates—is conceptually very different from the EE, which measures the observer’s lack of information about the quantum state of the system in an inaccessible region of spacetime. This approach allows to reduce the computation of the black hole EE to calculations in a field theory where spacetime geometry is not dynamical.
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