Dimensional reduction from entanglement in Minkowski space

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.

9 pages, changes to presentation, some content corrections, version published in JHEP

References in corpus (5)

• The Trouble with de Sitter Space
• Inside the Horizon with AdS/CFT
• Area-scaling of quantum fluctuations
• Thermodynamics and area in Minkowski space: Heat capacity of entanglement
• Implications of area scaling of quantum fluctuations

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