On the Background Method and the Renormalization of the Dirichlet Functional in the AdS/CFT

The Dirichlet background field method for the case of the fields belonging to a noncompact symmetric space is discussed. A specific feature of the Dirichlet boundary problem for the corresponding Laplace equation is the specification of the initial data on the characteristic manifold whose dimension can be less then the dimension of the geometrical boundary. The renormalization of the Dirichlet functional and breakdown of conformal invariance are discussed.