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We use holographic methods to characterize the RG flow of quantum informationin a Chern-Simons theory coupled to massive fermions. First, we useentanglement entropy and mutual information between strips to derive thedimension of the RG-driving operator and a monotonic c-function. We thendisplay a scaling regime where, unlike in a CFT, the mutual information betweenstrips changes non-monotonically with strip width, vanishing in both IR and UVbut rising to a maximum at intermediate scales. The associated informationtransitions also contribute to non-monotonicity in the conditional mutualinformation which characterizes the independence of neighboring strips afterconditioning on a third. Finally, we construct a measure of extensivity whichtests to what extent information that region A shares with regions B and C isadditive. In general, mutual information is super-extensive in holographictheories, and we might expect super-extensivity to be maximized in CFTs sincethey are scale-free. Surprisingly, our massive theory is more super-extensivethan a CFT in a range of scales near the UV limit, although it is lesssuper-extensive than a CFT at all lower scales. Our analysis requires the fullten-dimensional dual gravity background, and the extremal surfaces computingentanglement entropy explore all of these dimensions.

Information flows in strongly coupled ABJM theory