Boundary states as holographic duals of trivial spacetimes

Abstract

We study real-space quantum entanglement included in conformally invariant boundary states in conformal field theories (CFTs). We argue that boundary states essentially have no real-space entanglement, except for constant contributions from long range topological entanglement, by computing the entanglement entropy when the system is bipartition into two spatial regions. From the viewpoint of classical gravity duals in holography, this shows that boundary states are dual to trivial spacetimes of zero space-time volume. We also point out that a continuous multiscale entanglement renormalization ansatz (cMERA) for any CFTs can be formulated by employing a boundary state as its infrared unentangled state with an appropriate regularization. Exploiting this idea, we propose an approximation scheme of cMERA construction for general CFTs.