Entanglement entropy in all dimensions
Date
2015-12-15
Authors
Braunstein, Samuel L.
Das, Saurya
Shankaranarayanan, S.
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Abstract
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.
Description
Sherpa Romeo green journal. Open access. Creative Commons Attribution License (CC BY 4.0) applies.
Keywords
Entanglement , Entropy , Quantum field , Black hole entropy , Entanglement entropy , Black holes , Models of quantum gravity
Citation
Braunstein, S. L., Das, S., & Shankaranarayanan, S. (2013). Journal of High Energy Physics, 2013, 130. https://doi.org/10.1007/JHEP07(2013)130