On excited states in real-time AdS/CFT

TL;DR

This paper studies the Skenderis-van Rees holographic prescription for excited states in AdS/CFT, deriving formulas for correlators and inner products, and shows these states are coherent, impacting the understanding of wave functionals in AdS quantum gravity.

Contribution

It provides a detailed holographic analysis of excited states in AdS/CFT, establishing their coherent state nature and extending the Hartle-Hawking construction.

Findings

Excited states correspond to coherent states in AdS-Hilbert space.

Derived holographic formulas for correlators and inner products.

Confirmed the consistency of the Skenderis-van Rees prescription with known frameworks.

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.