A comment on multiple vacua, particle production and the time dependent AdS/CFT correspondence

TL;DR

This paper formulates a time-dependent AdS/CFT correspondence with multiple vacua, demonstrating how cosmological particle production affects correlators, illustrated through bubble spacetimes and the role of de Sitter alpha vacua.

Contribution

It provides an explicit framework for the time-dependent AdS/CFT correspondence with multiple vacua, including calculations of two-point functions in complex spacetime backgrounds.

Findings

Different amplitudes are related by cosmological particle production.

Explicit calculations in bubble spacetimes show the role of vacua.

Alpha vacua of de Sitter space appear naturally in the analysis.

Abstract

We give an explicit formulation of the time dependent AdS/CFT correspondence when there are multiple vacua present in 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.