Entanglement Entropy of Two Spheres
Abstract
We study the entanglement entropy SAB of a massless free scalar field on two spheres A and B whose radii are R1 and R2, 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 SA;B:=SA+SB-SAB is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r>>R1,R2, where SA and SB 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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