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Entropy 2011, 13(7), 1305-1323; doi:10.3390/e13071305
Article

State Operator Correspondence and Entanglement in AdS2/CFT1

Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019, India
Received: 13 June 2011 / Accepted: 22 June 2011 / Published: 19 July 2011
(This article belongs to the Special Issue Black Hole Thermodynamics)
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Abstract

Since Euclidean global AdS2 space represented as a strip has two boundaries, the state-operator correspondence in the dual CFT1 reduces to the standard map from the operators acting on a single copy of the Hilbert space to states in the tensor product of two copies of the Hilbert space. Using this picture we argue that the corresponding states in the dual string theory living on AdS2 × K are described by the twisted version of the Hartle–Hawking states, the twists being generated by a large unitary group of symmetries that this string theory must possess. This formalism makes natural the dual interpretation of the black hole entropy—as the logarithm of the degeneracy of ground states of the quantum mechanics describing the low energy dynamics of the black hole, and also as an entanglement entropy between the two copies of the same quantum theory living on the two boundaries of global AdS2 separated by the event horizon.
Keywords: black hole; statistical entropy; entanglement entropy black hole; statistical entropy; entanglement entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sen, A. State Operator Correspondence and Entanglement in AdS2/CFT1. Entropy 2011, 13, 1305-1323.

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