Next Article in Journal / Special Issue
Partition Function of the Schwarzschild Black Hole
Previous Article in Journal
Calculating the Prior Probability Distribution for a Causal Network Using Maximum Entropy: Alternative Approaches
Previous Article in Special Issue
Is Gravity an Entropic Force?
Entropy 2011, 13(7), 1305-1323; doi:10.3390/e13071305

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)
View Full-Text   |   Download PDF [155 KB, uploaded 24 February 2015]   |   Browse Figures


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 (CC BY 3.0).

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote |
MDPI and ACS Style

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

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here


[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert