Finite N and the failure of bulk locality: Black holes in AdS/CFT

Understand

We consider bulk quantum fields in AdS/CFT in the background of an eternal black hole.

• We show that for black holes with finite entropy, correlation functions of semiclassical bulk operators close to the horizon deviate from their semiclassical value and are ill-defined inside the horizon.
• This is due to the large-time behavior of correlators in a unitary CFT, and means the region near and inside the horizon receives corrections.
• We give a prescription for modifying the definition of a bulk field in a black hole background, such that one can still define operators that mimic the inside of the horizon, but at the price of violating microcausality.