Strong Subadditivity and Emergent Surface

TL;DR

This paper introduces bounds on entanglement entropy in quantum field theory, showing their relation to emergent surfaces in holographic duals and highlighting conditions for their equality.

Contribution

It presents the concepts of Upper and Lower Differential Entropy bounds and links strong subadditivity to emergent gravitational surfaces in holography.

Findings

Bounds are equal under translational invariance and smooth entropy variation.

Strong subadditivity implies the existence of an emergent gravitational surface.

Bounds precisely match the gravitational entropy of the emergent surface.

Abstract

In this paper, we introduce two bounds which we call the Upper Differential Entropy and the Lower Differential Entropy for an infinite family of intervals(strips) in quantum field theory. The two bounds are equal provided that the theory is translational invariant and the entanglement entropy varies smoothly with respect to the interval. When the theory has a holographic dual, strong subadditivity of entanglement entropy indicates that there is always an emergent surface whose gravitational entropy is exactly given by the bound.