Boundary conditions for conformally coupled scalar in AdS4

Abstract

We consider conformally coupled scalar with [Formula: see text] coupling in [Formula: see text] 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 [Formula: see text] coupling [Formula: see text] up to [Formula: see text] 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.