Abstract
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. The outcome of this study has remarkable implications on generalizing the Hartle-Hawking construction for wave functionals of excited states in AdS quantum gravity.
Highlights
The Skenderis-van Rees prescription, which allows the calculation of timeordered correlation functions of local operators in CFT’s using holographic methods is studied and applied for excited states
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 coherent states in the AdS-Hilbert space
We computed the time ordered 1- and 2-point functions in arbitrary states and have found a noticeable expression to calculate the inner product between them, which can be computed in the semi-classical approximation
Summary
In the Lorentzian setup φL denotes the (asymptotic) boundary condition for Φ at the timelike boundary The problem with this formula is that a priori, one does not have a precise prescription for the values of φΣ±, nor the form of the initial/final states described by the wave functionals Ψ0[φΣ±] on the Σ± surfaces. The projection of the state in the bulk configuration basis is given by the expression within the parenthesis on the r.h.s. of the equation (3.4), which agrees with the proposal (2.6) This remarkably generalizes the HH method to asymptotically AdS spacetimes, since it allows to define and evaluate In a forthcoming paper, this aspect and its consequences in quantum gravity will be explored more in depth
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