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We consider a real Klein-Gordon field in the Poincar\'e patch of$(d+1)$-dimensional anti-de Sitter spacetime, PAdS$_{d+1}$, and imposedynamical boundary condition on the asymptotic boundary of PAdS$_{d+1}$ thatdepend explicitly on the second time derivative of the field at the boundary.These boundary conditions are of generalized Wentzell type. We construct theWightman two-point function for the ground state of the Klein-Gordon theorywhenever the parameters of the theory (the field mass, curvature coupling andboundary condition parameters) render such ground state admissible. In thecases in which the mass of the Klein-Gordon field and the curvature couplingterm yield an effectively massless theory, we can define a boundary field whosedynamics are ruled by the dynamical boundary condition and construct, inaddition to the Wightman function for the Klein-Gordon field,boundary-to-boundary, boundary-to-bulk and bulk-to-boundary propagators.

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