Defect extremal surface as the holographic counterpart of Island formula

TL;DR

The paper introduces defect extremal surface (DES) as the holographic counterpart to the boundary quantum extremal surface (QES) in a defect AdS/CFT setting. DES augments the RT area term with the defect entropy and minimizes over bulk surfaces intersecting the defect, and its predictions are shown to reproduce boundary QES results in AdS/BCFT. By decomposing the bulk with a brane and applying brane-world holography, the authors derive a consistent 2d effective theory that yields a QES description on the boundary, reproducing island-like entanglement structure in a static setup. The work provides a concrete holographic framework for island physics on brane-worlds and suggests natural generalizations to more general brane embeddings and time-dependent scenarios.

Abstract

We propose defect extremal surface as the holographic counterpart of boundary quantum extremal surface. The defect extremal surface is defined by minimizing the Ryu-Takayanagi surface corrected by the defect theory. This is particularly interesting when the RT surface crosses or terminates on the defect. In a simple set up of AdS/BCFT, we find that the defect extremal surface formula gives precisely the same results of the boundary quantum extremal surface. We provide a decomposition procedure of an AdS bulk with a defect brane to see clearly how Island formula emerges from a brane world system with gravity glued to a flat space quantum field theory.

Figures (8)

• Figure 2.1: Holographic dual of a BCFT$_2$ defined on half space $(x>0)$.
• Figure 3.1: DES in original BCFT treated as the RT surface in BCFT$'$.
• Figure 3.2: Defect extremal surface in the disconnected phase.
• Figure 4.1: Bulk decomposition by inserting an imaginary boundary $Q'$.
• Figure 4.2: Effective description with Neumann boundary condition.