Defect extremal surfaces for entanglement negativity

TL;DR

This paper introduces a defect extremal surface (DES) approach within a holographic framework to compute entanglement negativity, demonstrating its equivalence to the island formula and analyzing its time evolution in black hole scenarios.

Contribution

It proposes a novel defect extremal surface formula for entanglement negativity in the defect AdS/BCFT setting, extending the semi-classical island formula and analyzing dynamic cases.

Findings

The DES formula matches the island formula for entanglement negativity.

Demonstrates the equivalence of DES and island formula in AdS$_3$/BCFT$_2$.

Analyzes the time evolution and Page curves of negativity in black hole models.

Abstract

We propose a doubly holographic version of the semi-classical island formula for the entanglement negativity in the framework of the defect AdS/BCFT correspondence where the AdS bulk contains a defect conformal matter theory. In this context, we propose a defect extremal surface (DES) formula for computing the entanglement negativity modified by the contribution from the defect matter theory on the end-of-the-world brane. The equivalence of the DES proposal and the semi-classical island formula for the entanglement negativity is demonstrated in AdS$_3$/BCFT$_2$ framework. Furthermore, in the time-dependent AdS$_3$/BCFT$_2$ scenarios involving eternal black holes in the lower dimensional effective description, we investigate the time evolution of the entanglement negativity through the DES and the island formulae and obtain the analogues of the Page curves.