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Entanglement Entropy of Two Spheres

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arxiv 1201.4865 v4 pith:7BGS5A3M submitted 2012-01-23 hep-th astro-ph.HEgr-qcquant-ph

classification hep-thastro-ph.HEgr-qcquant-ph
keywords entanglemententropyspheresfieldfreemasslessrespectivelyresult
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We study the entanglement entropy S_{AB} of a massless free scalar field on two spheres A and B whose radii are R_1 and R_2, respectively, and the distance between the centers of them is r. The state of the massless free scalar field is the vacuum state. We obtain the result that the mutual information S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r>>R_1,R_2, where S_A and S_B are the entanglement entropy on the inside region of A and B, respectively. We discuss possible connections of this result with the physics of black holes.

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