On excited states in real-time AdS/CFT

Understand

The Skenderis-van Rees prescription, which allows the calculation of time-ordered correlation functions of local operators in CFT's using holographic methods is studied and applied for excited states.

• Calculation of correlators and matrix elements of local CFT operators between generic in/out states are carried out in global Lorentzian AdS.
• We find the precise form of such states, obtain an holographic formula to compute the inner product between them, and using the consistency with other known prescriptions, we argue that the in/out excited states built according to the Skenderis-Van Rees prescription correspond to {\it coherent} states in the (large-$N$) AdS-Hilbert space.
• This is confirmed by explicit holographic computations.