Mutual Information of Two Distant Spheres and Expressions for Entropy in Nearly Conformal Gaussian Field Theories

Abstract

A new method is presented for computing low energy expansions for the entropy of approximately conformal states. We use this method to compute the mutual information of two distant spheres in a massless scalar field and find that the lowest order term agrees with existing results found with other methods. We also use our method to compute the entropy difference of massless scalar fields thermalized at a low temperature on the unit sphere. In particular, we find that the lowest order term for the entropy difference is proportional to the surface area of the sphere and we show that such an area law generally appears in a low energy expansion for the entropy difference.