Ground state for the Klein-Gordon field in anti-de Sitter spacetime with dynamical Wentzell boundary conditions

We consider a real Klein-Gordon field in the Poincaré patch of (d+1)-dimensional anti-de Sitter spacetime, PAdSd+1, and impose a dynamical boundary condition on the asymptotic boundary of PAdSd+1 that depends explicitly on the second time derivative of the field at the boundary. This boundary condition is of generalized Wentzell type. We construct the Wightman two-point function for the ground state of the Klein-Gordon theory whenever the parameters of the theory (the field mass, curvature coupling, and boundary condition parameters) render such a ground state admissible. In the cases in which the mass of the Klein-Gordon field and the curvature coupling term yield an effectively massless theory, we can define a boundary field whose dynamics are ruled by the dynamical boundary condition and construct, in addition to the Wightman function for the Klein-Gordon field, boundary-to-boundary, boundary-to-bulk, and bulk-to-boundary propagators.