Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole

Abstract

In this paper, we study the entanglement entropy between two SYK systems with bilinear coupling. We use the replica trick to calculate the entanglement entropy in the ground state. In parallel, we calculate the entanglement entropy through the Ryu-Takayanagi formula in gravity. For the ground state that is dual to an eternal traversable wormhole in AdS_2, the bulk quantum correction to the entanglement entropy is of the same order as the minimal surface area. The ground state of the coupled system is close to a thermofield double state with particular temperature and they have the same entanglement entropy. From the gravity point of view, we explain why the two states have the same entanglement entropy. We also study a case with time-dependent coupling, which involves finding the quantum extremal surface in the bulk.

42 pages, 9 figures. v2: References added

References in corpus (9)

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• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Relative entropy and the Bekenstein bound
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Cited by in corpus (10)

• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Holevo Information and Ensemble Theory of Gravity
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Black holes Entangled by Radiation
• Floquet SYK wormholes
• Gas of baby universes in JT gravity and matrix models
• Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models
• More on Complex Sachdev-Ye-Kitaev Eternal Wormholes
• Off-diagonal coupling of supersymmetric SYK model
• Josephson junction formed in the wormhole space time from the analysis for the critical temperature of Bose-Einstein condensate