State Operator Correspondence and Entanglement in AdS_2/CFT_1

TL;DR

This paper explores the state/operator correspondence in AdS_2/CFT_1, linking boundary states to entanglement and black hole entropy via twisted Hartle-Hawking states in string theory.

Contribution

It introduces a formalism connecting boundary states in AdS_2/CFT_1 to twisted Hartle-Hawking states, elucidating the entanglement structure and entropy interpretation.

Findings

States in dual string theory are described by twisted Hartle-Hawking states.

Black hole entropy is interpreted as entanglement entropy between two boundary theories.

The formalism links ground state degeneracy to entanglement in the dual quantum mechanics.

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 x K are described by 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.