Boundary conditions for conformally coupled scalar in AdS$_4$

Abstract

We consider conformally coupled scalar with $ϕ^4$ 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 $ϕ^4$ coupling $λ$ up to $λ^2$ 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.

1+9 pages, a few typos are corrected