Mutual Information of Generalized Free Fields

We study generalized free fields (GFF) from the point of view of information measures. We first review conformal GFF, their holographic representation, and the ambiguities in the assignation of algebras to regions that arise in these theories. Then we study the mutual information (MI) in several geometric configurations. The MI displays unusual features at the short distance limit: a leading volume term rather than an area term, and a logarithmic term in any dimensions rather than only for even dimensions as in ordinary CFT's. We find the dependence of some subleading terms on the conformal dimension $\Delta$ of the GFF. We study the long distance limit of the MI for regions with boundary in the null cone. The pinching limit of these surfaces show the GFF behaves as an interacting model from the MI point of view. The pinching exponents depend on the choice of algebra. The entanglement wedge algebra choice allows these models to ``fake'' causality, giving results consistent with its role in the description of large $N$ models.