Dimensional reduction from entanglement in Minkowski space

TL;DR

This paper provides evidence that quantum correlations and fluctuations within any sub-volume of Minkowski space exhibit surface area scaling, indicating a form of dimensional reduction related to entanglement in quantum field theory.

Contribution

It demonstrates that correlation functions and energy fluctuations in Minkowski space scale with surface area, revealing a novel form of dimensional reduction linked to entanglement.

Findings

Correlation functions scale as the surface area of the sub-volume.

Energy fluctuations of a massless field exhibit area scaling.

Bulk fluctuations can be represented by a boundary theory at high temperature.

Abstract

Using a quantum field theoretic setting, we present evidence for dimensional reduction of any sub-volume of Minkowksi space. First, we show that correlation functions of a class of operators restricted to a sub-volume of D-dimensional Minkowski space scale as its surface area. A simple example of such area scaling is provided by the energy fluctuations of a free massless quantum field in its vacuum state. This is reminiscent of area scaling of entanglement entropy but applies to quantum expectation values in a pure state, rather than to statistical averages over a mixed state. We then show, in a specific case, that fluctuations in the bulk have a lower-dimensional representation in terms of a boundary theory at high temperature.