Boundary States as Holographic Duals of Trivial Spacetimes

TL;DR

This paper demonstrates that boundary states in conformal field theories have negligible real-space entanglement and are holographically dual to trivial spacetimes, and proposes a new cMERA approximation scheme using boundary states.

Contribution

It shows boundary states are essentially unentangled and dual to trivial spacetimes, and introduces a novel cMERA construction method employing boundary states as unentangled IR states.

Findings

Boundary states have negligible real-space entanglement.

Boundary states are dual to trivial spacetimes with zero volume.

A new cMERA approximation scheme using boundary states is proposed.

Abstract

We study real-space quantum entanglement included in conformally invariant boundary states in conformal field theories (CFTs). First, we argue that boundary states essentially have no real-space entanglement by computing the entanglement entropy when we bipartite the system into two spatial regions. From the viewpoint of holography, this shows that boundary states are dual to trivial spacetimes of zero spactime volume. Next, we 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.