AdS${}_3$ Vacuum State from Four Minkowski Vacuum States

We show that a tensor product of four specific $1+2$ Minkowski vacuum states is a self-consistent vacuum state for an infinite set of three-dimensional anti-de Sitter (AdS${}_3$) spacetimes if their parity and time-reversal symmetry are broken in a particular way. The infinite set consists of pairs of all AdS${}_3$ with non-zero unique scalar curvatures.