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

Island on codimension-two branes in AdS/dCFT