The Wave Function of Vasiliev's Universe - A Few Slices Thereof

TL;DR

This paper analyzes the partition function of a specific conformal field theory related to higher-spin gravity in de Sitter space, revealing divergences and potential instabilities of de Sitter space in quantum gravity.

Contribution

It computes the partition function of the Sp(N) CFT on various geometries and explores its implications for the wave function of the universe and de Sitter stability.

Findings

Partition function diverges at large negative mass and small S1.

Partition function peaks at zero squashing.

Divergences suggest de Sitter instability in higher-spin gravity.

Abstract

We study the partition function of the free Sp(N) conformal field theory recently conjectured to be dual to asymptotically de Sitter higher-spin gravity in four-dimensions. We compute the partition function of this CFT on a round sphere as a function of a finite mass deformation, on a squashed sphere as a function of the squashing parameter, and on an S2xS1 geometry as a function of the relative size of S2 and S1. We find that the partition function is divergent at large negative mass in the first case, and for small $S^1$ in the third case. It is globally peaked at zero squashing in the second case. Through the duality this partition function contains information about the wave function of the universe. We show that the divergence at small S1 occurs also in Einstein gravity if certain complex solutions are included, but the divergence in the mass parameter is new. We suggest an interpretation for this divergence as indicating an instability of de Sitter space in higher spin gravity, consistent with general arguments that de Sitter space cannot be stable in quantum gravity.