Page curve from defect extremal surface and island in higher dimensions

Abstract

Abstract 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.

Keywords

• AdS-CFT Correspondence
• Gauge-gravity correspondence
• Holography and condensed matter physics (AdS/CMT)