Entanglement entropy in all dimensions

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Braunstein, Samuel L.
Das, Saurya
Shankaranarayanan, S.
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It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann entropy. Here we show that the R´enyi entropy provides a convergent alternative, yielding a quantitative measure of entanglement between quantum field theoretic degrees of freedom inside and outside hypersurfaces. For the first time, we show that the entanglement entropy in higher dimensions is proportional to the higher dimensional area. We also show that the R´enyi entropy diverges at specific values of the R´enyi parameter q in each dimension, but this divergence can be tamed by introducing a mass to the quantum field.
Sherpa Romeo green journal. Open access. Creative Commons Attribution License (CC BY 4.0) applies.
Entanglement , Entropy , Quantum field , Black hole entropy , Entanglement entropy , Black holes , Models of quantum gravity
Braunstein, S. L., Das, S., & Shankaranarayanan, S. (2013). Journal of High Energy Physics, 2013, 130. https://doi.org/10.1007/JHEP07(2013)130