On the Dynamics in the AdS/BCFT Correspondence

TL;DR

This paper explores perturbations in the AdS/BCFT framework, deriving mode expansions for tensionless branes and identifying energy-momentum constraints, revealing how BCFTs couple to gravity with different boundary conditions.

Contribution

It provides explicit mode expansions for perturbations in tensionless ETW branes and uncovers new energy-momentum constraints for BCFTs coupled to gravity with specific boundary conditions.

Findings

Mode expansion derived for tensionless ETW branes.

Energy-momentum constraints for BCFTs with gravity coupling.

BCFT coupling depends on brane tension and boundary conditions.

Abstract

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 AdSd+1 spaectime where d is larger than 2. 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.