Holographic Dual of BCFT
We propose a holographic dual of a conformal field theory defined on a manifold with boundaries, i.e. boundary conformal field theory (BCFT). This new holography successfully calculates the boundary entropy or g-function in two dimensional BCFTs and it agrees with the finite part of the holographic entanglement entropy. Moreover, we can naturally derive a holographic g-theorem. We conjecture a higher dimensional analogue of g-theorem and give some evidences from both the gravity and field theory side. We also discuss the gravity dual with boundaries with arbitrary shape.