Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence
Diptarka Das, Sumit R. Das, Antal Jevicki, Qibin Ye
TL;DR
The paper constructs a bi-local collective-field theory for the singlet sector of the Lorentzian Sp(2N) vector model and shows its Hamiltonian matches the O(N) case up to signs, with a crucial negative saddle point that necessitates a Grassmann-aware quantization.By relating the O(N) collective construction to higher-spin bulk fields in AdS and implementing a double analytic continuation, the authors map the Sp(2N) theory to higher-spin gravity in de Sitter space and develop a bulk-space interpretation via a bi-local representation and a geometric pseudo-spin Hilbert space.Nonperturbative quantization is enabled by a Kahler (pseudo-spin) representation, which imposes a finite bi-local Hilbert space consistent with the fermionic exclusion principle at finite N and yields a coupling G = 1/N that naturally regulates the theory.The work provides a concrete framework for Sp(2N)/dS higher-spin holography, outlines the necessary sign structures in correlators and vertices, and discusses implications for dS entropy and potential generalizations to other dimensions and string-theoretic contexts.
Abstract
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.