Conformal boundary condition and massive gravitons in AdS/BCFT

According to Witten [1], the conformal boundary condition of gravity, which specifies geometry and trace extrinsic curvature, is elliptic leads well-defined perturbation theory gravity about any classical solution. The was previously considered in [2, 3] context AdS/BCFT, wherein equation motion end-of-the-world derived emphasized. In this paper, we investigate further other consequences AdS/BCFT. We derive central charges holographic Weyl anomaly show that they are exactly same for Dirichlet condition. analysis metric with (CBC), (DBC) Neumann (NBC) imposed on brane admit an interpretation as fluctuation curvature (case CBC DBC) induced NBC) Q respectively. all cases, modes massive, closely relevant massive island formation literature. Our results reveal there non-trivial gravitational dynamics from curvatures branes, may have interesting applications island. also discuss, passing, localization gravitons world theory. find that, contrary NBC, graviton CBC/DBC located non-positive tension instead non-negative tension.