Higher Spin de Sitter Holography from Functional Determinants

TL;DR

This paper explores the higher spin dS/CFT correspondence by numerically analyzing the partition function of the free Sp(N) model, revealing insights into the Hartle-Hawking wavefunctional and its maxima related to de Sitter space.

Contribution

It introduces a numerical method to compute the partition function for deformations in higher spin dS/CFT and interprets the results in terms of the wavefunctional and double trace deformations.

Findings

The wavefunctional has a local maximum near the pure de Sitter vacuum.

Other maxima can correspond to inhomogeneous and anisotropic configurations.

Fixing certain bulk scalar averages makes the wavefunction normalizable.

Abstract

We discuss further aspects of the higher spin dS/CFT correspondence. Using a recent result of Dunne and Kirsten, it is shown how to numerically compute the partition function of the free Sp(N) model for a large class of SO(3) preserving deformations of the flat/round metric on R^3/S^3 and the source of the spin-zero single-trace operator dual to the bulk scalar. We interpret this partition function as a Hartle-Hawking wavefunctional. It has a local maximum about the pure de Sitter vacuum. Restricting to SO(3) preserving deformations, other local maxima (which exceed the one near the de Sitter vacuum) can peak at inhomogeneous and anisotropic values of the late time metric and scalar profile. Numerical experiments suggest the remarkable observation that, upon fixing a certain average of the bulk scalar profile at I^+, the wavefunction becomes normalizable in all the other (infinite) directions of the deformation. We elucidate the meaning of double trace deformations in the context of dS/CFT as a change of basis and as a convolution. Finally, we discuss possible extensions of higher spin de Sitter holography by coupling the free theory to a Chern-Simons term.