  The bulk to boundary mapping for massive scalar fields is constructed,
providing a de Sitter analog of the LSZ reduction formula. The set of boundary
correlators thus obtained defines a potentially new class of conformal field
theories based on principal series representations of the global conformal
group. Conversely, we show bulk field operators in de Sitter may be
reconstructed from boundary operators. While consistent at the level of the
free field theory, the boundary CFT does not satisfy cluster decomposition. The
resulting conformal field theory does not satisfy the basic axioms of Euclidean
quantum field theory due to Osterwalder and Schrader, so is likely not
well-defined once interactions are included.
