Area-scaling of quantum fluctuations

TL;DR

This paper demonstrates that quantum fluctuations of bulk operators confined to a region scale with the surface area of that region, supporting holographic principles and area-scaling phenomena in quantum field theory.

Contribution

It establishes that two-point functions of certain bulk operators scale with the boundary area, independent of the region's shape, revealing a fundamental area-scaling property.

Findings

Two-point functions scale with boundary area

Scaling is independent of region geometry

Implications for holography and Unruh radiation

Abstract

We show that fluctuations of bulk operators that are restricted to some region of space scale as the surface area of the region, independently of its geometry. Specifically, we consider two point functions of operators that are integrals over local operator densities whose two point functions falls off rapidly at large distances, and does not diverge too strongly at short distances. We show that the two point function of such bulk operators is proportional to the area of the common boundary of the two spatial regions. Consequences of this, relevant to the holographic principle and to area-scaling of Unruh radiation are briefly discussed.