Implications of area scaling of quantum fluctuations

TL;DR

This paper investigates the area scaling of quantum fluctuations in Minkowski space-time and provides evidence that such scaling originates from an underlying boundary theory, supported by mathematical proofs and examples.

Contribution

It demonstrates that the area scaling of quantum fluctuations can be attributed to a boundary theory, with proofs of covariance scaling and illustrative examples.

Findings

Quantum fluctuations exhibit area scaling in Minkowski space.

Covariance between operators scales linearly with boundary area.

Boundary theories can explain non-monotonous volume-area relationships.

Abstract

Quantum fluctuations of a certain class of bulk operators defined in spatial sub-volumes of Minkowski space-time, have an unexpected area scaling property. We wish to present evidence that such area scaling may be ascribed to a boundary theory. We first highlight the implications of area scaling with two examples in which the boundary area of the spatial regions is not monotonous with their volume. Next, we prove that the covariance of two operators that are restricted to two different regions in Minkowski space scales linearly with their mutual boundary area. Finally, we present an example which demonstrates why this implies an underlying boundary theory.