Island on codimension-two branes in AdS/dCFT

TL;DR

This paper investigates the properties of the island and holography on codimension-two branes in AdS/dCFT, revealing how graviton localization and black hole entropy evolution differ from the codimension-one case.

Contribution

It extends island and double holography studies to codimension-two branes, analyzing graviton spectrum, localization, and black hole Page curves in this new setting.

Findings

Graviton mass decreases with increasing brane tension.

Massless graviton mode is forbidden by boundary or normalization conditions.

Page curve is recovered despite the extremal surface passing the horizon after some time.

Abstract

The previous studies of the island and double holography mainly focus on codimension-one branes. This paper explores the island on the codimension-two brane in AdS/dCFT. The codimension-two brane is closely related to conical singularity, which is very different from the codimension-one brane. We analyze the mass spectrum of gravitons on the codimension-two brane and find that the larger the brane tension is, the smaller the gravitational mass is. The massless mode is forbidden by either the boundary or normalization conditions. We prove that the first massive gravitational mode is located on the codimension-two brane; the larger the tension, the better the localization. It is similar to the case of codimension-one brane and builds an excellent physical foundation for the study of black hole evolution on codimension-two branes. We find that the Page curve of eternal black holes can be recovered due to the island ending on the codimension-two brane. The new feature is that the extremal surface passing the horizon cannot be defined after some finite time in the no-island phase. Fortunately, this unusual situation does not affect the Page curve since it happens after Page time.