Implications of area scaling of quantum fluctuations

Quantum fluctuations of a certain class of bulk operators defined in spatial subvolumes of Minkowski space-time have an unexpected area scaling property. We 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 monotonic with their volume. Next, we show that the covariance of two operators that are restricted to two different regions in Minkowski space scale linearly with their mutual boundary area. Finally, we present an example which demonstrates why this implies an underlying boundary theory.