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arXiv · hep-th/0302186

Dimensional reduction from entanglement in Minkowski space

Ram Brustein·Amos Yarom
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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.

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Ram Brustein, Amos Yarom. 2005-02-09. Dimensional reduction from entanglement in Minkowski space. https://doi.org/10.1088/1126-6708%2F2005%2F01%2F046

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