Bounds on CFT correlations from the thermal partition function
Fikret Ceyhan, Thomas Faulkner
TL;DR
This paper establishes upper bounds on mutual information in conformal field theories using the thermal partition function, linking phase transitions in AdS/CFT to entanglement measures.
Contribution
It introduces bounds on CFT mutual information derived from the modular nuclearity condition and relates them to geometric duals in AdS/CFT.
Findings
Bounds are consistent with AdS/CFT geometric duals.
Links between Hawking-Page transition and entanglement wedge transition.
Proposes a new boundary quantity for minimal entanglement wedge distance.
Abstract
We discuss upper bounds on the mutual information for disjoint spherical regions of the CFT vacuum. To prove our bounds, we utilize the modular nuclearity condition, which is in turn related to finiteness of the thermal partition function of the CFT. Our bounds are satisfied by the conjectured geometric duals of these correlation measures in AdS/CFT, where they link the Hawking-Page phase transition with the entanglement wedge phase transition. We use these results to conjecture a new boundary theory quantity that computes the minimal distance between two general entanglement wedges.
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