Journal of High Energy Physics · 2021

Defect extremal surface as the holographic counterpart of Island formula

Feiyu Deng · Jinwei Chu · Yang Zhou

Introduced the defect extremal surface prescription and showed how the boundary quantum extremal surface emerges from a brane-world construction.

Defect extremal surface as the holographic counterpart of Island formula abstract structural diagram

Abstract

We propose defect extremal surface as the holographic counterpart of boundary quantum extremal surface. The prescription minimizes a Ryu–Takayanagi surface corrected by the quantum theory localized on the defect and reproduces the boundary quantum extremal surface result in a simple AdS/BCFT setup.

Context

Island calculations combine a gravitational area term with quantum entropy. A holographic defect supplies a geometric setting in which the two contributions can be tracked together.

Main result

The defect extremal surface minimizes an RT surface corrected by defect quantum matter. In the AdS/BCFT example it reproduces the boundary quantum extremal surface result through a bulk decomposition procedure.

SDES=extΓ[Area(Γ)4GN+Sdefect]S_{\mathrm{DES}}=\operatorname*{ext}_{\Gamma}\left[\frac{\mathrm{Area}(\Gamma)}{4G_N}+S_{\mathrm{defect}}\right]
Schematic form of the published defect extremal surface prescription: extremize the area term plus defect entropy.

Why it matters

It gives the island prescription a concrete holographic counterpart and a geometric language for comparing bulk and brane-world descriptions.

Citation / BibTeX
@article{Deng:2021DESIsland,
  author = {Deng, Feiyu and Chu, Jinwei and Zhou, Yang},
  title = {Defect extremal surface as the holographic counterpart of Island formula},
  journal = {JHEP},
  volume = {03},
  pages = {008},
  year = {2021},
  doi = {10.1007/JHEP03(2021)008},
  eprint = {2012.07612},
  archivePrefix = {arXiv}
}