  We derive a collective field theory of the singlet sector of the Sp(2N) sigma
model. Interestingly the hamiltonian for the bilocal collective field is the
same as that of the O(N) model. However, the large-N saddle points of the two
models differ by a sign. This leads to a fluctuation hamiltonian with a
negative quadratic term and alternating signs in the nonlinear terms which
correctly reproduces the correlation functions of the singlet sector. Assuming
the validity of the connection between O(N) collective fields and higher spin
fields in AdS, we argue that a natural interpretation of this theory is by a
double analytic continuation, leading to the dS/CFT correspondence proposed by
Anninos, Hartman and Strominger. The bi-local construction gives a map into the
bulk of de Sitter space-time. Its geometric pseudospin-representation provides
a framework for quantization and definition of the Hilbert space. We argue that
this is consistent with finite N grassmanian constraints, establishing the
bi-local representation as a nonperturbative framework for quantization of
Higher Spin Gravity in de Sitter space.
