cMERA as Surface/State Correspondence in AdS/CFT

TL;DR

This paper explores the surface/state correspondence in AdS3/CFT2 using a generalized cMERA framework, linking boundary states to bulk geometry and operators, and analyzing the information metric of excited states.

Contribution

It extends the cMERA formulation to AdS3/CFT2, incorporating boundary states and bulk diffeomorphisms, and identifies bulk operators and metrics within this setup.

Findings

Bulk local operators reproduce scalar field solutions in AdS3.

The information metric of excited states matches that of 2D hyperbolic space.

The formulation naturally accounts for bulk diffeomorphisms.

Abstract

We present how the surface/state correspondence, conjectured in arXiv:1503.03542, works in the setup of AdS3/CFT2 by generalizing the formulation of cMERA. 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 AdS3 and bulk scalar propagators. We also calculate the information metric for a locally excited state and show that it is given by that of 2d hyperbolic manifold, which is argued to describe the time slice of AdS3.