Properties of Causal Holographic Information

TL;DR

This paper studies the properties of causal holographic information in AdS/CFT, revealing a new conformal invariant and exploring its relation to central charges and potential CFT counterparts.

Contribution

It identifies a novel conformal invariant in causal holographic information and analyzes its behavior under higher curvature corrections in the bulk.

Findings

Discovered a universal conformal invariant in the divergence coefficient.

Connected the invariant to the a and c central charges in 4D.

Proposed a possible CFT quantity corresponding to causal holographic information.

Abstract

Causal holographic information [1] is a variant of the Ryu-Takayanagi proposal for the entanglement entropy of a spatial region in the context of AdS/CFT, but with the bulk surface defined by causality rather than extremality. We investigate the properties of causal holographic information, focusing in particular on the universal coefficient of the logarithmically divergent term. We find that this coefficient contains a novel conformal invariant that cannot be written as an integral of local quantities. By considering higher curvature corrections in the bulk, we identify the coefficient of the a and c central charges in 4 dimensions. Finally, we speculate about which CFT quantity could correspond to the causal holographic information.