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

TL;DR

This paper constructs the ground state and propagators for a Klein-Gordon field in anti-de Sitter spacetime with novel dynamical Wentzell boundary conditions, extending the understanding of boundary effects in quantum fields.

Contribution

It introduces and analyzes dynamical boundary conditions of Wentzell type for Klein-Gordon fields in AdS, providing explicit ground state constructions and propagators.

Findings

Constructed the Wightman two-point function for the ground state.

Derived boundary-to-boundary, boundary-to-bulk, and bulk-to-boundary propagators.

Extended the framework to effectively massless theories with boundary dynamics.

Abstract

We consider a real Klein-Gordon field in the Poincar\'e patch of $(d+1)$-dimensional anti-de Sitter spacetime, PAdS$_{d+1}$, and impose dynamical boundary condition on the asymptotic boundary of PAdS$_{d+1}$ that depend explicitly on the second time derivative of the field at the boundary. These boundary conditions are 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 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.