Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Correspondence

We present how the surface-state correspondence, conjectured by Miyaji and Takayanagi, works in the setup of ${\mathrm{AdS}}_3/{\mathrm{CFT}}_2$ by generalizing the formulation of a continuous multiscale entanglement renormalization group ansatz. The boundary states in conformal field theories play a crucial role in our formulation and the bulk diffeomorphism is naturally taken into account. We give an identification of bulk local operators which reproduces correct scalar field solutions on ${\mathrm{AdS}}_3$ and bulk scalar propagators. We also calculate the information metric for a locally excited state and show that it reproduces the time slice of ${\mathrm{AdS}}_3$.