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Flavored N=4 SYM -- a highly entangled quantum liquid

We study N=4 SYM theory coupled to fundamental N=2 hypermultiplets in a state of finite charge density. The setup can be described holographically as a configuration of D3 and D7 branes with a non-trivial worldvolume gauge field on the D7. The phase has been identified as a new form of quantum liquid, where certain properties are those of a Fermi liquid while others are clearly distinct. We focus on the entanglement among the flavors, as quantified by the entanglement entropy. The expectation for a Fermi liquid would be a logarithmic enhancement of the area law, but we find a more drastic enhancement instead. The leading contributions are volume terms with a non-trivial shape dependence, signaling extensive entanglement among the flavors. At finite temperature these correlations are confined to a region of size given by the inverse temperature.