Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions

Abstract

We consider a real, massive scalar field on ${\mathrm{PAdS}}_{d+1}$, the Poincaré domain of the $(d+1)$-dimensional anti-de Sitter (AdS) spacetime. We first determine all admissible boundary conditions that can be applied on the conformal boundary, noting that there exist instances where "bound states" solutions are present. Then, we address the problem of constructing the two-point function for the ground state satisfying those boundary conditions, finding ultimately an explicit closed form. In addition, we investigate the singularities of the resulting two-point functions, showing that they are consistent with the requirement of being of Hadamard form in every globally hyperbolic subregion of ${\mathrm{PAdS}}_{d+1}$ and proposing a new definition of Hadamard states which applies to ${\mathrm{PAdS}}_{d+1}$.

arXiv comment30 pages, 2 figures. Publication version

References in corpus (14)

• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
• Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum
• Vacua, Propagators, and Holographic Probes in AdS/CFT
• Quantum Field Theory on Curved Backgrounds -- A Primer
• Cosmological horizons and reconstruction of quantum field theories
• States of Low Energy on Robertson-Walker Spacetimes
• Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property
• Hadamard renormalized scalar field theory on anti-de Sitter space-time
• A remark on alpha vacua for quantum field theories on de Sitter space
• On the construction of Hartle-Hawking-Israel states across a static bifurcate Killing horizon
• Stueckelberg massive electromagnetism in de Sitter and anti-de Sitter spacetimes: Two-point functions and renormalized stress-energy tensors
• States of Low Energy in Homogeneous and Inhomogeneous, Expanding Spacetimes
• On the Hartle-Hawking-Israel states for spacetimes with static bifurcate Killing horizons

Cited by in corpus (34)

• Superradiance in the BTZ black hole with Robin boundary conditions
• Ground states of a Klein-Gordon field with Robin boundary conditions in global anti-de Sitter spacetime
• Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type
• Stationary scalar clouds around a BTZ black hole
• Unruh-DeWitt detector in dimensionally-reduced static spherically symmetric spacetimes
• Algebraic quantum field theory on spacetimes with timelike boundary
• On the algebraic quantization of a massive scalar field in anti-de-Sitter spacetime
• Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions
• Superradiant instabilities in the Kerr-mirror and Kerr-AdS black holes with Robin boundary conditions
• Comments on the anti-Hawking effect on a BTZ black hole spacetime
• Comment on "Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions"
• Ground and thermal states for the Klein-Gordon field on a massless hyperbolic black hole with applications to the anti-Hawking effect
• The holographic Hadamard condition on asymptotically Anti-de Sitter spacetimes
• Ground State for the Klein-Gordon field in anti-de Sitter spacetime with dynamical Wentzell boundary conditions
• Boundary Conditions and Vacuum Fluctuations in ${\mathrm{AdS}}_4$
• 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
• Boundary-to-bulk maps for AdS causal wedges and RG flow
• The time traveler's guide to the quantization of zero modes
• Robin boundary conditions in acoustic BTZ black holes
• Quantum Scattering on a Cone revisited
• Analog model for the BTZ black hole
• Vacuum densities and the Casimir forces for branes orthogonal to the AdS boundary
• Renormalisation in maximally symmetric spaces and semiclassical gravity in Anti-de Sitter spacetime
• Quantum Approach to Bound States in Field Theory
• Hidden freedom in the mode expansion on static spacetimes
• Finite temperature charge and current densities around a cosmic string in AdS spacetime with compact dimension
• Spatially flat FLRW spacetimes with a Big Bang from matrix geometry
• Boundary conditions for isolated asymptotically anti-de Sitter spacetimes
• Propagators in curved spacetimes from operator theory
• Particle detectors under chronological hazard
• Unstable mode and the Unruh-DeWitt detector
• Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
• Physical significance of generalized boundary conditions: an Unruh-DeWitt detector viewpoint on ${\text{AdS}}_2\times {\mathbb{S}}^2$