Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type

Abstract

We study a real, massive Klein-Gordon field in the Poincaré fundamental domain of the $(d+1)$-dimensional anti-de Sitter (AdS) spacetime, subject to a particular choice of dynamical boundary conditions of generalized Wentzell type, whereby the boundary data solves a non-homogeneous, boundary Klein-Gordon equation, with the source term fixed by the normal derivative of the scalar field at the boundary. This naturally defines a field in the conformal boundary of the Poincaré fundamental domain of AdS. We completely solve the equations for the bulk and boundary fields and investigate the existence of bound state solutions, motivated by the analogous problem with Robin boundary conditions, which are recovered as a limiting case. Finally, we argue that both Robin and generalized Wentzell boundary conditions are distinguished in the sense that they are invariant under the action of the isometry group of the AdS conformal boundary, a condition which ensures in addition that the total flux of energy across the boundary vanishes.

arXiv comment12 pages, 1 figure. In V3: refs. added, introduction and conclusions expanded

References in corpus (13)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Lectures on holographic methods for condensed matter physics
• Lecture Notes on Holographic Renormalization
• Quantum Geometry and Black Hole Entropy
• Green's function approach to Chern-Simons extended electrodynamics: an effective theory describing topological insulators
• Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions
• Self-adjoint extensions of the Laplace-Beltrami operator and unitaries at the boundary
• On Self-adjoint extensions and symmetries in Quantum Mechanics
• On the algebraic quantization of a massive scalar field in anti-de-Sitter spacetime
• Generalized Wentzell boundary conditions and quantum field theory
• Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions
• Quantization of scalar fields coupled to point-masses
• Boundary Hilbert spaces and trace operators

Cited by in corpus (18)

• Ground states of a Klein-Gordon field with Robin boundary conditions in global anti-de Sitter spacetime
• Comments on the anti-Hawking effect on a BTZ black hole spacetime
• Ground and thermal states for the Klein-Gordon field on a massless hyperbolic black hole with applications to the anti-Hawking effect
• Ground State for the Klein-Gordon field in anti-de Sitter spacetime with dynamical Wentzell boundary conditions
• Fundamental solutions and Hadamard states for a scalar field with arbitrary boundary conditions on an asymptotically AdS spacetimes
• Quantum field theory with dynamical boundary conditions and the Casimir effect: Coherent states
• Vacuum polarization on topological black holes with Robin boundary conditions
• A short review of the Casimir effect with emphasis on dynamical boundary conditions
• On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary
• Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions
• On Maxwell's Equations on Globally Hyperbolic Spacetimes with Timelike Boundary
• Spatially flat FLRW spacetimes with a Big Bang from matrix geometry
• Renormalisation in maximally symmetric spaces and semiclassical gravity in Anti-de Sitter spacetime
• Hidden freedom in the mode expansion on static spacetimes
• Propagators in curved spacetimes from operator theory
• Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
• Meronic Einstein-Yang-Mills black hole in 5D and gravitational spin from isospin effect
• The cost of building a wall for a fermion