Boundary Conditions and Vacuum Fluctuations in $\mathrm{AdS}_4$

Understand

Initial conditions given on a spacelike, static slice of a non-globally hyperbolic spacetime may not define the fates of classical and quantum fields uniquely.

• Such lack of global hyperbolicity is a well-known property of the anti-de Sitter solution and led many authors to question how is it possible to develop a quantum field theory on this spacetime.
• Wald and Ishibashi took a step towards the healing of that causal issue when considering the propagation of scalar fields on AdS.
• They proposed a systematic procedure to obtain a physically consistent dynamical evolution.