Abstract
We consider a real Klein-Gordon field in the Poincaré patch of ()-dimensional anti–de Sitter spacetime, , and impose a dynamical boundary condition on the asymptotic boundary of 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.
- Received 17 March 2022
- Accepted 27 April 2022
DOI:https://doi.org/10.1103/PhysRevD.105.105017
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Published by the American Physical Society