Defect Extremal Surface for Reflected Entropy

TL;DR

This paper introduces a defect extremal surface formula for reflected entropy in AdS/BCFT, demonstrating its equivalence to the island formula and applying it to black hole evaporation scenarios.

Contribution

It proposes a new defect extremal surface formula for reflected entropy and proves its equivalence to the island formula in specific holographic models.

Findings

Defect extremal surface formula matches island formula results.

The formula accurately describes reflected entropy evolution in black hole models.

Demonstrates the applicability of defect extremal surfaces in holographic entanglement calculations.

Abstract

Defect extremal surface is defined by extremizing the Ryu-Takayanagi formula corrected by the quantum defect theory. This is interesting when the AdS bulk contains a defect brane (or string). We introduce a defect extremal surface formula for reflected entropy, which is a mixed state generalization of entanglement entropy measure. Based on a decomposition procedure of an AdS bulk with a brane, we demonstrate the equivalence between defect extremal surface formula and island formula for reflected entropy in AdS$_3$/BCFT$_2$. We also compute the evolution of reflected entropy in evaporating black hole model and find that defect extremal surface formula agrees with island formula.