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. The study of the relations between Quantum Field Theories (QFT’s) in different dimensions has come recently to the general attention. Some of the most interesting and intriguing developments of QFT and string theory, like Maldacena’s ADS/CFT conjecture [1, 2] and t’Hooft’s [3] and Susskind’s [4] holographic principle, seem to indicate that relations of this kind are going to play a fundamental role in understanding QFT and string theory. In this letter we point out a relation that exists between Minkowski QFT and de Sitter QFT in one dimension less. We show that the “preferred” [5, 6] de Sitter Klein–Gordon field of squared mass λ arises by averaging in a well-defined sense an ordinary Klein– Gordon field of mass M living in the Minkowski ambient spacetime and, vice versa, the Klein–Gordon field in the ambient Minkowski spacetime can be obtained by superposing fields in the lower dimensional de Sitter manifold.