Defect extremal surface for reflected entropy

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)/BCFT2. We also compute the evolution of reflected entropy in evaporating black hole model and find that defect extremal surface formula agrees with island formula.

Automated summary

The defect extremal surface formula, the island formula for reflected entropy, and their equivalence are introduced and studied in this paper. It is found that the defect extremal surface formula agrees with the island formula in AdS spaces with defect branes.