Holographic entanglement and causal information in coherent states

Scalar solitons in global AdS4 are holographically dual to coherent states carrying a non-trivial condensate of a scalar operator. We study the holographic information content of these states, focusing on a particular spatial region, by examining the entanglement entropy and causal holographic information. We show generically that whenever the dimension of the condensed operator is sufficiently low (characterized by the double-trace operator becoming relevant), such coherent states have lower entanglement and causal holographic information than the vacuum state of the system, despite having greater energy. We also use these geometries to illustrate the fact that causal wedges associated with a simply-connected boundary region can have non-trivial topology even in causally trivial spacetimes.

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