$\phi^4$-Model and Holography in Four Dimensions

TL;DR

This paper explores the holographic correspondence for a conformally coupled $^4$-model in four dimensions, deriving correlator generating functions and exact classical solutions in various conformally invariant scalar field theories.

Contribution

It provides the first derivation of boundary correlators for the $^4$-model in (A)dS4 using conformal mappings and presents new exact solutions for nonlinear wave equations in multiple dimensions.

Findings

Generated boundary correlators up to first order in coupling.

Obtained exact classical solutions for $^3$, $^4$, and $^6$ models.

Established connections between conformally coupled scalars in different spacetimes.

Abstract

The generating function of correlators of dual operators on the boundary of (A)dS4 space corresponding to the conformally coupled $\phi^4$-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) $\phi^3$, $\phi^4$ and $\phi^6$-models in D=6,4,3 Euclidean/Minkowski (AdS/dS) spaces are obtained.