Interacting fields in real-time AdS/CFT

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.