The phase of de Sitter higher spin gravity

TL;DR

This paper investigates the phase of the de Sitter higher spin gravity partition function, finding that the total phase vanishes for non-minimal Vasiliev theories, supporting a consistent state counting interpretation.

Contribution

It computes the total phase of Vasiliev higher spin gravity on the sphere by summing over all spins and regularizing the infinite sum, showing the phase vanishes for non-minimal theories.

Findings

Total phase vanishes for non-minimal Vasiliev theories.

Regularization schemes yield consistent results.

Supports a state counting interpretation of the partition function.

Abstract

The one-loop Euclidean partition function on the sphere is known to exhibit a nontrivial phase for massless fields of spin greater than one. Such a phase appears to be in tension with a state counting interpretation of the partition function and its relation to the de Sitter entropy. It has been recently argued that the phase associated with the gravitational path integral can be cancelled by including the contribution of an observer. In this note, we compute the total phase of Vasiliev higher spin gravity on the sphere by summing over the contributions of all spins. We evaluate the resulting infinite sum using two different regularization schemes, obtaining consistent results. We find that for the non-minimal Vasiliev theory, which includes massless fields of all integer spins, the total phase vanishes in all dimensions. This result suggests that the sphere partition function of these theories may be consistent with a counting interpretation, without explicitly including an observer.