We formulate a first quantized construction of the AdS d+1 /CFT d correspondence using the bi-local representation of the free d-dimensional large-N vector model. The earlier reconstruction of AdS 4 higher spin gravity provides a scheme where the AdS spacetime (and higher spin fields) is given by the composite bi-local fields. The underlying first quantized, world-sheet picture is extracted in the present work and generalized to any dimension. A higher spin AdS particle model is shown to emerge from the collective biparticle system of Minkowski particles through a canonical transformation. As such, this construction provides a simple explicit mechanism of the AdS/CFT 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 bilocal 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 Grassmannian constraints, establishing the bi-local representation as a nonperturbative framework for quantization of Higher Spin Gravity in de Sitter space. 1

Following the work of Maldacena and Zhiboedov, we study the implementation of the Coleman–Mandula theorem in the free O(N)/higher spin correspondence. In the bi-local framework we first define an S-matrix for scattering of collective dipoles. Its evaluation in the case of free UV fixed point theory leads to the result S = 1 stated in the title. We also present an appropriate field transformation that is seen to transform away all the nonlinear 1/N interactions of this theory. A change of boundary conditions and/or external potentials results in a nontrivial theory.