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 funda- mental 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 vac- uum 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 commuta- tions 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.
Highlights
Introduction and summaryFinding a precise and complete theory of quantum gravity has been a longstanding problem
We propose a complete microscopic definition of the Hilbert space of minimal higher spin de Sitter quantum gravity and its Hartle-Hawking vacuum state
For certain systems living in an infinitely deep gravitational potential well, shaped by a negative vacuum energy density, this problem has been solved: the Hilbert space and operator algebra of these theories are those of a conformal field theory living on the boundary of the well [1]
Summary
Finding a precise and complete theory of quantum gravity has been a longstanding problem. There have been several efforts to go beyond four-dimensional low energy effective field theory, towards a fundamental theory of quantum gravity in universes with a positive vacuum energy density These include, but are certainly not limited to, string theory constructions of metastable de Sitter vacua [17,18,19,20], holographic considerations of the de Sitter observer’s static region [21,22,23,24,25,26,27,28,29,30], more general holographic considerations of the landscape [31,32,33,34,35], and the dS-CFT correspondence [36,37,38]. A list of symbols that summarizes our notation is included in appendix C
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