# Entanglement Entropy after Double-Excitation as Interaction Measure

## TL;DR

This paper investigates how entanglement entropy evolves after double local quenches in 2D conformal field theories, revealing a negative correction due to gravitational attraction in holographic duals.

## Contribution

It introduces a novel analysis of entanglement entropy after double excitations in 2D CFTs, incorporating a fusion matrix approach for multi-point conformal blocks.

## Key findings

- Entanglement growth is not additive for double quenches.
- A negative correction term is identified, interpreted as gravitational attraction.
- The method involves a special limit of 6-point functions and fusion matrix techniques.

## Abstract

We study entanglement entropy after a double local quench in two-dimensional conformal field theories (CFTs), with any central charge $c>1$. In the holographic CFT, such a state with double-excitation is dual to an AdS space with two massive particles introduced from the boundary. We show that the growth after the double local excitations cannot be given by the sum of two local quenches but with an additional negative term. This negative contribution can be naturally interpreted as due to the attractive force of gravity. In CFT side, this evaluation of the entanglement entropy is accomplished by a special limit of 6-point functions, where we employed the fusion matrix approach for multi-point conformal blocks developed in arXiv:1905.02191.