# Disentangling the thermofield-double state

## TL;DR

This paper analyzes how the entanglement entropy of the thermofield-double state evolves under double-traced operators, revealing saturation behavior and coherence effects, with implications for black hole dynamics in AdS/CFT.

## Contribution

It provides a detailed computation of entanglement entropy evolution under double-traced operators in large N theories, including strong coupling and Schwarzian limits, linking boundary operators to bulk black hole geometry.

## Key findings

- Entanglement entropy saturates after thermal time due to exponential decay.
- Coherence of double-traced operators inferred from entropy equality.
- Black hole size changes correspond to operator actions in AdS/CFT.

## Abstract

In this paper, we consider the evolution of the thermofield-double state under the double-traced operator that connects its both sides. We will compute the entanglement entropy of the resulting state using the replica trick for the large N field theory. To leading order, it can be computed from the two-point function of the theory, where, in CFTs, it is fixed by the symmetries. Due to the exponential decay of the interaction, the entanglement entropy saturates about the thermal time after the interaction is on. Next, we restrict ourselves to one dimension and assume that the theory at strong coupling is effectively described by the Schwarzian action. We then compute the coarse-grained entropy of the resulting state using the four-point function. The equality of the two entropies implies that the double-traced operators in our theory act coherently. In AdS/CFT correspondence where the thermofield-double state corresponds to a two-sided black hole, the action of a double-traced operator corresponds to shrinking or expanding the black hole in the bulk.