TL;DR
This paper investigates the entanglement entropy between two spheres in a massless scalar field vacuum, revealing a cutoff-independent mutual information proportional to their areas at large separation, with implications for black hole physics.
Contribution
It provides an analytical calculation of the mutual information between two spheres, showing its independence from ultraviolet cutoff and proportionality to their areas at large distances.
Findings
Mutual information is independent of ultraviolet cutoff.
Mutual information is proportional to the product of the spheres' areas.
Results have potential implications for black hole physics.
Abstract
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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