# Time Evolution of Entanglement Negativity from Black Hole Interiors

## TL;DR

This paper studies how entanglement negativity evolves over time after a global quench in a 1+1D conformal field theory, using holography and black hole geometries, and finds exact agreement with CFT calculations.

## Contribution

It provides a holographic description of the time evolution of entanglement negativity for mixed states in a 1+1D CFT following a global quench, matching CFT results.

## Key findings

- Holographic entanglement negativity matches CFT computations.
- Time evolution follows from black hole geodesic structures.
- Results apply to mixed states of disjoint and adjacent intervals.

## Abstract

We investigate the time evolution of entanglement negativity following a global quench for mixed state configurations of two disjoint and adjacent intervals in a ($1+1$)-dimensional conformal field theory ($CFT_{1+1}$) dual to the eternal black hole sliced in half by an end of the world brane, through the $AdS_3/CFT_2$ correspondence. To this end we obtain the time evolution of the holographic entanglement negativity for such mixed states from a dual bulk eternal black hole geometry and elucidate the relevant geodesic structures. The holographic entanglement negativity for such mixed states, following a global quench is described by half of the results for the eternal black hole. Significantly, in this case our holographic results match exactly with the corresponding $CFT_{1+1}$ computations.