Remark on multiple vacua, particle production, and the time-dependent AdS/CFT correspondence

We give an explicit formulation of the time dependent AdS/CFT correspondence when there are multiple vacua present in the Lorentzian signature. By computing sample two point functions we show how different amplitudes are related by cosmological particle production. We illustrate our methods in two example spacetimes: (a) a “bubble of nothing” in AdS space, and (b) an asymptotically locally AdS spacetime with a bubble of nothing on the boundary. In both cases the $\alpha$ vacua of de Sitter space make an interesting appearance.