Holographic mutual information and distinguishability of Wilson loop and defect operators

Understand

The mutual information of disconnected regions in large $N$ gauge theories with holographic gravity duals can undergo phase transitions.

• These occur when connected and disconnected bulk Ryu-Takayanagi surfaces exchange dominance.
• That is, the bulk `soap bubble' snaps as the boundary regions are drawn apart.
• We give a gauge-theoretic characterization of this transition: States with and without a certain defect operator insertion -- the defect separates the entangled spatial regions -- are shown to be perfectly distinguishable if and only if the Ryu-Takayanagi surface is connected.