${\varphi }^4$-Model and Holography in Four Dimensions

Abstract

The generating function of correlators of dual operators on the boundary of (A)dS4 space corresponding to the conformally coupled ${\varphi }^4$-model is obtained up to first order in the coupling constant by using the conformal map between massless scalar fields in (Euclidean) Minkowski space and conformally coupled scalars on (Euclidean anti) de Sitter space. Some exact classical solutions of the nonlinear wave equation of massless (conformally coupled) ${\varphi }^3$, ${\varphi }^4$ and ${\varphi }^6$-models in D=6,4,3 Euclidean/Minkowski (AdS/dS) spaces are obtained.

Appendix B including two eps figures is added where the identities necessary for section 3 are worked out. Furthermore a diagrammatic approach to calculate higher order terms in the perturbation series is given