Boundary conditions for conformally coupled scalar in AdS${}_4$

Abstract

We consider conformally coupled scalar with ${\varphi }^4$ 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 ${\varphi }^4$ 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.

1+9 pages, a few typos are corrected

References in corpus (1)

• Boundary conditions for SU(2) Yang-Mills on $Ad{S}_4$