On the dynamics in the AdS/BCFT correspondence

We consider a perturbation of the Einstein gravity with the Neumann boundary condition, which is regarded as an end of the world brane (ETW brane) of the AdS/BCFT correspondence, in the AdS(d+1) spacetime with d >= 3. We obtain the mode expansion of the perturbations explicitly for the tensionless ETW brane case. We also show that the energy-momentum tensor in a d-dimensional BCFT should satisfy nontrivial constraints other than the ones for the boundary conformal symmetry if the BCFT can couple to a d-dimensional gravity with a specific boundary condition, which can be the Neumann or the conformally Dirichlet boundary conditions. We find these constraints are indeed satisfied for the free scalar BCFT. For the BCFT in the AdS/BCFT, we find that the BCFT can couple to the gravity with the Neumann boundary condition for the tensionless brane, but the BCFT can couple to the gravity with the conformally Dirichlet boundary condition for the nonzero tension brane by using holographic relations.

Automated summary

In this study, we investigate a perturbation of the Einstein gravity with the Neumann boundary condition, which is considered as an end of the world brane (ETW brane) in the AdS(d+1) spacetime. We explicitly obtain the mode expansion of the perturbations for the tensionless ETW brane case. Furthermore, we analyze the constraints that the energy-momentum tensor in a d-dimensional BCFT should satisfy if it can couple to a d-dimensional gravity with a specific boundary condition, such as the Neumann or conformally Dirichlet boundary conditions. We find that these constraints are satisfied for the free scalar BCFT and the BCFT in the AdS/BCFT can couple to the gravity with the Neumann or conformally Dirichlet boundary condition.