Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence

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.