Localization of Negative Energy and the Bekenstein Bound

TL;DR

This paper demonstrates that negative energy cannot be isolated far from positive energy in conformal field theories, aligning with the Bekenstein bound and using relative entropy to refine localization constraints.

Contribution

It introduces a new form of the Bekenstein bound based on relative entropy monotonicity, improving negative energy localization limits.

Findings

Negative energy cannot be isolated far from positive energy in CFTs.

A new Bekenstein bound based on relative entropy is established.

The bound is highly insensitive to space-time entanglement.

Abstract

A simple argument shows that negative energy cannot be isolated far away from positive energy in a conformal field theory and strongly constrains its possible dispersal. This is also required by consistency with the Bekenstein bound written in terms of the positivity of relative entropy. We prove a new form of the Bekenstein bound based on the monotonicity of the relative entropy, involving a "free" entropy enclosed in a region which is highly insensitive to space-time entanglement, and show that it further improves the negative energy localization bound.