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Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity

by Victoria L. Martin, Andrew Svesko

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Andrew Svesko
Submission information
Preprint Link:  (pdf)
Date accepted: 2020-09-03
Date submitted: 2020-07-03 02:00
Submitted by: Svesko, Andrew
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


In this note we compute the 1-loop partition function of spin-$s$ fields on Euclidean de Sitter space $S^{2n+1}$ using the quasinormal mode method. Instead of computing the quasinormal mode frequencies from scratch, we use the analytic continuation prescription $L_{\text{AdS}}\to iL_{\text{dS}}$, appearing in the dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on thermal $\text{AdS}_{2n+1}$ into the quasinormal mode frequencies of fields on de Sitter space. We compare the quasinormal mode and heat kernel methods of calculating 1-loop determinants, finding exact agreement, and furthermore explicitly relate these methods via a sum over the conformal dimension. We discuss how the Wick rotation of normal modes on thermal $\text{AdS}_{2n+1}$ can be generalized to calculating 1-loop partition functions on the thermal spherical quotients $S^{2n+1}/\mathbb{Z}_{p}$. We further show that the quasinormal mode frequencies encode the group theoretic structure of the spherical spacetimes in question, analogous to the recent analysis made for thermal AdS in (1910.07607) and (1910.11913).

List of changes

-- Further clarification around $\text{Poly}(\Delta)$, particularly how it is uncovered generally and why it may be ignored in our case
-- Rename Dirichlet boundary conditions to boundary conditions periodic in Euclidean time
-- Typos fixed

Published as SciPost Phys. 9, 039 (2020)

Reports on this Submission

Anonymous Report 2 on 2020-8-26 (Invited Report)


1. As mentioned before, the analysis is a straightforward illustration of known techniques. It would have been better if there was more novelty present. The one-loop determinants have already been calculated using the heat-kernel approach in the past and an agreement is expected using this (by now) well-established techniques of QNMs. Nonetheless, the analysis shown in the paper is correct.


The authors have addressed my queries and have made appropriate additions to the manuscript. I recommend this article for publication.

  • validity: ok
  • significance: ok
  • originality: low
  • clarity: good
  • formatting: good
  • grammar: good

Anonymous Report 1 on 2020-7-21 (Invited Report)


1) The paper is concise

2) Reproduces a previous calculation while using a streamlined method


The authors changes are appropriate and the paper should be published.

  • validity: high
  • significance: good
  • originality: good
  • clarity: good
  • formatting: excellent
  • grammar: perfect

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