# Interacting fields in real-time AdS/CFT

## TL;DR

This paper computes time-ordered correlation functions in a holographic AdS/CFT setup with scalar interactions, revealing how bulk interactions deform excited states and providing insights into n-point functions between these states.

## Contribution

It introduces a method to compute time-ordered correlators with scalar self-interactions in a mixed Euclidean-Lorentzian AdS setup, connecting bulk interactions to boundary state deformations.

## Key findings

- 3-point correlators match previous Euclidean AdS results
- Cubic interactions deform excited states into squeezed states
- Diagrammatic approach suggests properties of n-point functions between excited states

## Abstract

We compute time-ordered 2- and 3-pt correlation functions of CFT scalar operators between generic in/out states. The calculation is holographically carried out by considering a non backreacting AdS scalar field with a $\lambda \phi^3$ self-interaction term on a combination of Euclidean and Lorentzian AdS sections following the Skenderis-van Rees prescription. We show that, although working in an essentially different set up, the final result for the 3-pt correlators agree with those of Rastelli et al. for Euclidean AdS. By analyzing the inner product between the in/out excited states in the large $N$ approximation, we argue that a cubic bulk interaction deforms the excited states from coherent into \emph{squeezed}. Finally, a diagrammatic interpretation of the results suggests some general properties for the $n$-point correlation functions between excited states.