Subregion-subregion Duality in AdS/CFT

February 6, 2018
11:30am to 1:00pm

Room 218

Specialist level
Ritam Sinha

Room 218


Since the discovery of the RT formula, the relation between geometry and quantum information theory (QIT) has been a subject of intense investigation.

An important ingredient to calculate most of these QIT quantities in the CFT is the reduced density matrix (RDM). It is therefore of great interest to try and understand what part of the bulk geometry it corresponds to. In this light, we shall review two very different approaches towards understanding the bulk dual of the RDM. The first paper we review is by Harlow et. al. who propose that the bulk dual of a CFT can be understood as a quantum error correcting code. We shall try to understand what this implies for the subregion- subregion duality. The next paper we review is by Maldacena et. al. who forward the proposal that the CFT relative entopy (RE) is the same as the bulk RE upto geometries that are differ from the AdS-Poincare to linear order in the density matrix. This proposal also has implications towards understanding the bulk dual of the RDM. The final paper is again by Harlow et. al. where they use Maldacena's proposal into the framework of quantum error correction to provide more evidence that the bulk dual of the RDM is the entanglement wedge as opposed to the Causal wedge.