Boundary conditions for conformally coupled scalar in AdS$_4$

TL;DR

This paper investigates boundary conditions for a conformally coupled scalar in AdS$_4$, deriving perturbative solutions, boundary correlators, and effects of marginal deformations within the AdS/CFT framework.

Contribution

It provides perturbative solutions up to second order in coupling and explores boundary conditions and marginal deformations in AdS$_4$ for the scalar field.

Findings

Computed 2, 4, and 6-point functions for different boundary conditions.

Derived boundary effective actions under marginal deformation.

Analyzed the impact of boundary conditions on dual CFT correlators.

Abstract

We consider conformally coupled scalar with $\phi^4$ coupling in AdS$_4$ and study its various boundary conditions on AdS boundary. We have obtained perturbative solutions of equation of motion of the conformally coupled scalar with power expansion order by order in $\phi^4$ coupling $\lambda$ up to $\lambda^2$ order. In its dual CFT, we get 2,4 and 6 point functions by using this solution with Dirichlet and Neumann boundary conditions via AdS/CFT dictionary. We also consider marginal deformation on AdS boundary and get its on-shell and boundary effective actions.