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It is controversial whether entanglement islands can exist in massless gravity theories. Recently, it is found that the massless entanglement island appears in wedge holography with DGP gravity on the branes. In this paper, we generalize the discussions to the codim-n holography named cone holography. For simplicity, we focus on the case with a codim-2 E brane and a codim-1 Q brane. We discuss the effective action, mass spectrum and holographic entanglement entropy for cone holography with DGP terms. We verify that there is massless gravity on the branes, and recover non-trivial entanglement islands and Page curves. Besides, we work out the parameter space which allows entanglement islands and Page curves. Compared with wedge holography, there are several new features. First, one can not add DGP gravity on the codim-2 E brane. That is because the energy density has to be a constant on codim-2 branes for Einstein gravity in bulk. Second, the Hartman-Maldacena surface ends only on the codim-1 Q brane. Third, the Hartman-Maldacena surface can be defined only in a finite time. We notice that this unusual situation also appears in AdS/dCFT and even in AdS/CFT. Fortunately, it does not affect the Page curve since it happens after Page time. Our results provide more support that the entanglement island is consistent with massless gravity theories., Comment: 32 pages, 16 figures, minor revision published in JHEP

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., Comment: 46 pages, 20 figures, reference added, minor revision published in JHEP

In this paper, we investigate AdS/BCFT for curvature-squared gravity. To warm up, we start with Gauss-Bonnet gravity. We derive the one point function of stress tensor and show that the central charge related to the norm of displacement operator is positive for the couplings obeying causality constraints. Furthermore, by imposing the null energy condition on the end-of-the-world brane, we prove the holographic g-theorem for Gauss-Bonnet gravity. This corrects a wrong point of view in the literature, which claims that the holographic g-theorem is violated for Gauss-Bonnet gravity. As a by-product, we obtain the boundary entropy and A-type boundary central charges in general dimensions. We also study AdS/BCFT for general curvature-squared gravity. We find that it is too restrictive for the shape of the brane and the dual BCFT is trivial if one imposes Neumann boundary conditions for all of the gravitational modes. Instead, we propose to impose Dirichlet boundary condition for the massive graviton, while imposing Neumann boundary condition for the massless graviton. In this way, we obtain non-trivial shape dependence of stress tensor and well-defined central charges. In particular, the holographic g-theorem is satisfied by general curvature-squared gravity. Finally, we discuss the island and show that the Page curve can be recovered for Gauss-Bonnet gravity. Interestingly, there are zeroth-order phase transitions for the Page curve within one range of couplings obeying causality constraints. Generalizing the discussions to holographic entanglement entropy and holographic complexity in AdS/CFT, we get new constraints for the Gauss-Bonnet coupling, which is stronger than the causality constraint., Comment: 49 pages, 29 figures, revision accepted for publication in JHEP, main improvements: prove that our g-function can recover the universal term of boundary entropy in general dimensions; add a toy model to explain the novel zeroth-order phase transition of the Page curve analytically

Recently it is found that Weyl anomaly leads to new anomalous currents in an external electromagnetic field in the curved spacetime. For simplicity, the initial works mainly focus on weak gravitational fields and the anomalous current is obtained for conformally flat spaces with small scale factors. In this paper, we generalize the results to the case with arbitrary scale factors. Firstly, we derive the transformation law of current under Weyl transformation, from which one can read off the anomalous current in general conformally flat spaces. Secondly, by using the Weyl transformation of currents we provide a new derivation of the Weyl-anomaly-induced current near the boundary. Thus we have obtained the two kinds of anomalous currents in the literature from a unified formula. Finally, we extend the discussions to n-form fields and find similar anomalous currents., Comment: 18 pages, 0 figure, match the published version in PLB