State operator correspondence and entanglement in AdS 2/CFT 1

Abstract

Since Euclidean global AdS 2 space represented as a strip has two boundaries, the state-operator correspondence in the dual CFT 1 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 AdS 2 × 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 AdS 2 separated by the event horizon. © 2011 by the author; licensee MDPI, Basel, Switzerland.