Defect extremal surface as the holographic counterpart of Island formula

Feiyu Deng,Jinwei Chu,Yang Zhou

doi:10.1007/jhep03(2021)008

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 quantum extremal surface formula emerges from a brane world system with gravity glued to a flat space quantum field theory.

Highlights

Once promoted to be valid for general quantum system glued with gravity region, the quantum extremal surface (QES) formula seems very powerful
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 quantum extremal surface formula emerges from a brane world system with gravity glued to a flat space quantum field theory

Summary

Bulk defect extremal surface

If the tension of the Q brane is zero, the brane will be orthogonal to the asymptotic boundary, as denoted by the dashed line in figure 1. One can read off the Weyl factor from the induced metric on the brane, ds2brane = Ω−2(y)ds2flat, i.e. To compute the entanglement entropy of an interval [0, a] on the brane, one can use the one-point function of the twist operator Φn inserted at y = a [5]. The entanglement entropy of an interval [0, y1] on the brane can be computed from the one-point function with the limit of n → 1 as follows. For the boundary without physical degrees of freedom, we set log g = 0 From this result we see that the entanglement entropy of an interval including the boundary point on the brane is a constant. It does not depend on the length of the interval.

Bulk DES: the proposal

Boundary quantum extremal surface

Area term

Conclusion and discussion

A Boundary QES from replica wormhole

B Gluing conditions