Boundary entropy under ambient RG flow in the AdS/BCFT model

We discuss the change of the boundary entropy under an ambient renormalization group flow. We use conformal perturbation theory to calculate the change of the boundary entropy for $d$-dimensional BCFTs between two nearby fixed points. We also use the AdS${}_{d+1}$/BCFT${}_d$ model to calculate the boundary entropy. We show that the boundary entropy can increase under the ambient RG flow both in conformal perturbation theory and the AdS${}_{d+1}$/BCFT${}_d$ model. In a special case, the change of the boundary entropy in the AdS${}_{d+1}$/BCFT${}_d$ model reduces to that of the conformal perturbation theory.