# Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole

## TL;DR

This paper investigates the entanglement entropy between two coupled SYK models using both field theory and gravity approaches, revealing insights into the duality with eternal traversable wormholes and quantum extremal surfaces.

## Contribution

It provides a comparative analysis of entanglement entropy calculations via the replica trick and Ryu-Takayanagi formula, including quantum corrections and time-dependent coupling scenarios.

## Key findings

- Ground state entanglement entropy matches between SYK and gravity calculations.
- Quantum corrections are significant and comparable to minimal surface area.
- Time-dependent coupling involves quantum extremal surface analysis.

## 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.