Correspondence between Minkowski and de Sitter quantum field theory

In this letter we show that the “preferred” Klein–Gordon Quantum Field Theories (QFT's) on a d-dimensional de Sitter spacetime can be obtained from a Klein–Gordon QFT on a (d+1)-dimensional “ambient” Minkowski spacetime satisfying the spectral condition and, conversely, that a Klein–Gordon QFT on a (d+1)-dimensional “ambient” Minkowski spacetime satisfying the spectral condition can be obtained as superposition of d-dimensional de Sitter Klein–Gordon fields in the preferred vacuum. These results establish a correspondence between QFT's living on manifolds having different dimensions. The method exposed here can be applied to study other situations and notably QFT on Anti de Sitter spacetime.