Higher spin de Sitter Hilbert space

Abstract

We propose a complete microscopic definition of the Hilbert space of minimal higher spin de Sitter quantum gravity and its Hartle-Hawking vacuum state. The fundamental degrees of freedom are 2N bosonic fields living on the future conformal boundary, where N is proportional to the de Sitter horizon entropy. The vacuum state is normalizable.The model agrees in perturbation theory with expectations from a previously proposed dS-CFT description in terms of a fermionic Sp(N) model, but it goes beyond this, both in its conceptual scope and in its computational power. In particular it resolves the apparent pathologies affecting the Sp(N) model, and it provides an exact formula for late time vacuum correlation functions. We illustrate this by computing probabilities for arbitrarily large field excursions, and by giving fully explicit examples of vacuum 3-and 4-point functions. We discuss bulk reconstruction and show the perturbative bulk QFT canonical commutations relations can be reproduced from the fundamental operator algebra, but only up to a minimal error term ∼ e −O(N ) , and only if the operators are coarse grained in such a way that the number of accessible "pixels" is less than O(N ). Independent of this, we show that upon gauging the higher spin symmetry group, one is left with 2N physical degrees of freedom, and that all gauge invariant quantities can be computed by a 2N × 2N matrix model. This suggests a concrete realization of the idea of cosmological complementarity.

de Sitter future-past extremal surfaces and the entanglement wedge

“…In [11], a higher spin dS 4 duality was conjectured involving a 3-dim CFT of anti-commuting (ghost) scalars, which exemplifies this (see also e.g. [12]- [20]). While dual operator correlation functions are obtained by a differentiate prescription applied to Z CF T , bulk expectation values are obtained by weighting with the bulk probability |Ψ dS | 2 .…”

Bootstrapping inflationary correlators in Mellin space

“…For three-point correlators involving a generic triplet of spinning fields, there are various tensor structures consistent with conformal symmetry[23,[106][107][108] 16. The tensorial structure, which is fixed by conformal symmetry, re-produces existing expressions for spinning conformal structures in Fourier space e.g [29,104,[109][110][111][112]…”

Spinors in supersymmetric dS/CFT

“…We have seen that the fermionic contributions introduce an interesting N -dependence in the theory. dS/CFT at finite N is largely unexplored territory, but recently the Q-model [50,61] has been put forward as a possible completion of higher-spin dS/CFT. We made use of the measure implied by the Q-model to identify the domain of the wave function in some of the models we considered in this paper.…”

“…For the scalar deformation, we can identify the boundaries of the configuration space with a good degree of confidence. Here, the completion of dS/CFT of [50] which provides not just a wave function but also a Hilbert space and an inner product, directly applies to our model. It implies a measure that restricts the configuration space of the wave function to deformations with σ/ √ N > −3/4.…”