Page curve from defect extremal surface and island in higher dimensions
Jinwei Chu (Department of Physics, Fudan University, Shanghai, 200433, China, Department of Physics, University of Chicago, Chicago, Illinois, 60637, USA); Feiyu Deng (Department of Physics, Fudan University, Shanghai, 200433, China); Yang Zhou (Department of Physics, Fudan University, Shanghai, 200433, China, Peng Huanwu Center for Fundamental Theory, Hefei, Anhui, 230026, China)
Defect extremal surface (DES) is defined by minimizing the Ryu-Takayanagi surface corrected by the quantum theory localized on the defect, which is useful when the RT surface crosses or terminates on the defect. Based on the decomposition procedure of an AdS bulk with a defect brane, proposed in [69], we derive Page curve in a time dependent set up of AdS3/BCFT2, and find that the result from island formula agrees with defect extremal surface formula precisely. We then extend the study to higher dimensions and find that the entropy computed from bulk defect extremal surface is generally less than that from island formula in boundary low energy effective theory, which implies that the UV completion of island formula gives a smaller entropy.