De Sitter-invariant States from Holography

A class of invariant states under de Sitter isometries is constructed in d-dimensional Conformal Field Theories from the universal sector of AdS/CFT dualities. These states extend the Mottola-Allen $\alpha$-vacua to theories containing scalar primary operators of arbitrary scaling dimensions, and are proven to explicitly break conformal symmetry. Two-point correlators in these states are shown to satisfy a generalized spectral decomposition in terms of free massive propagators. It is also pointed out that the spectral decomposition of generic Euclidean correlators is known in the mathematics literature as Olevsky index transform, of which computational use can be made.