Large-N Collective Fields and de Sitter / CFT correspondence

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We derive the collective theory of singlet fields of large-N Sp(N) spin
models and display its unconventional features. Using the known relationship
between O(N) collective fields and higher spin fields of Vasiliev theory in AdS
space, we argue that the unique features of the Sp(N) collective
theory suggest an interpretation in terms of a higher spin theory in de Sitter
space, as proposed by Anninos, Hartman and Strominger.  This is
reminiscent of the way the Liouville mode is naturally  interpreted as
time in supercritical worldsheet string theory.