Revisiting recent progress in the Karch–Randall braneworld

Abstract Motivated by the study of entanglement island in the Karch–Randall braneworld, it has been conjectured and proven in general that entanglement island is not consistent with long-range (massless) gravity. In this paper, we provide a careful check of this conclusion in a model of massless gravity that is constructed using the Karch–Randall braneworld. We show that there is indeed no entanglement island and hence not a nontrivial Page curve due to the diffeomorphism invariance if we are studying the correct question. We will also clarify the subtlety that is important to put this question in a correct manner. Moreover, we show that this conclusion is not affected by deforming the set-up with the Dvali–Gabadadze–Porrati (DGP) terms. Furthermore, we show that the consistency of holography in this model will provide nontrivial constraints to the DGP parameters. This study provides an example that causality and holography in anti-de Sitter space can be used to constrain low energy effective theories. We also clarify several subtleties in the braneworld gravity which were overlooked in the literature. We show that a direct implication of these clarifications is a resolution of the causality paradox in the Karch–Randall braneworld. At the end, we discuss the robustness of the above results against possible coarse-graining protocols to define a subregion in a gravitational theory.