Modave lectures on bulk reconstruction in AdS/CFT

TL;DR

This paper reviews bulk reconstruction in AdS/CFT, highlighting quantum error correction, tensor network models, gauge invariance, and a specific method for AdS3/CFT2 involving cross-cap states.

Contribution

It synthesizes existing reconstruction methods, discusses quantum error correction in the bulk, and introduces a new approach for AdS3/CFT2 using cross-cap states.

Findings

Bulk operators can be reconstructed from CFT operators.

Bulk exhibits quantum error correcting properties.

A new reconstruction method for AdS3/CFT2 using cross-cap states.

Abstract

These lecture notes are based on a series of lectures given at the XIII Modave summer school in mathematical physics. We review the construction due to Hamilton, Kabat, Lifschytz and Lowe for reconstructing local bulk operators from CFT operators in the context of AdS/CFT and show how to recover bulk correlation functions from this definition. Building on the work of these authors, it has been noted that the bulk displays quantum error correcting properties. We will discuss tensor network toy models to exemplify these remarkable features. We will discuss the role of gauge invariance and of diffeomorphism symmetry in the reconstruction of bulk operators. Lastly, we provide another method of bulk reconstruction specified to AdS$_3$/CFT$_2$ in which bulk operators create cross-cap states in the CFT.