Defect extremal surface as the holographic counterpart of Island formula

TL;DR

This paper introduces defect extremal surfaces as a holographic analog of boundary quantum extremal surfaces, demonstrating their equivalence in AdS/BCFT setups and deriving the Island formula from a brane world perspective.

Contribution

It defines defect extremal surfaces and shows they match boundary quantum extremal surfaces, providing a new geometric understanding of the Island formula in holography.

Findings

Defect extremal surface formula matches boundary quantum extremal surface results.

Derived Island formula from a brane world system with gravity and quantum fields.

Provided a decomposition procedure for AdS bulk with defects.

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.