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 λϕ3 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 squeezed. Finally, a diagrammatic interpretation of the results suggests some general properties for the n-point correlation functions between excited states.
Highlights
For the case of vacuum to vacuum scattering amplitudes, the SvR prescription requires to consider a Lorentzian AdS cilinder ML smoothly glued to two halves of Euclidean AdS M± along the past/future spacelike surfaces Σ± that limit the Lorentzian region, as shown in figure 1(a)
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 squeezed
A diagrammatic interpretation of the results suggests some general properties for the n-point correlation functions between excited states
Summary
Let us consider the simplest example of interacting fields on a global AdS spacetime background: a real massive scalar field with a cubic self interaction, which should be enough to. When writing the third line we have used the equation of motion (2.2) These expressions are rather formal though, as an appropriate prescription is required for imposing the asymptotic boundary conditions on Φ to avoid divergences. While the first prescription leads to easier computations, the latter is more natural in the sense that it automatically meets the Ward identities between two and higher order point functions. With this in mind, we are going to follow the -prescription when treating the free contribution of the on-shell action and follow the asymptotic prescription in the interacting terms
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