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Normal modes in thermal AdS via the Selberg zeta function

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: 2020-07-14
Date submitted: 2020-07-09 02:00
Submitted by: Svesko, Andrew
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin $s$ fields on hyperbolic quotient spacetimes $\mathbb{H}^{3}/\mathbb{Z}$ are related via the Selberg zeta function. We extend that analysis to thermal $\text{AdS}_{2n+1}$ backgrounds, with quotient structure $\mathbb{H}^{2n+1}/\mathbb{Z}$. Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.

Author comments upon resubmission

See referee reply posted online.

List of changes

-- Added paragraph to discussion to further clarify the ambiguities with the even dimensional analysis.
-- We have added a paragraph in Appendix B just below Eq. (B.13), where provide the more intricate details relating Eq. (3.25) to Eq. (B.9) in the case of AdS_{5} for an arbitrary higher spin field.
-- We have expanded the discussion concerning the analysis of removing non-square integrable zero modes for higher spin fields in both the BTZ case and thermal AdS_{3}. We further clarify what would need to be shown for higher dimensional AdS solutions, but explain why we think the analysis is possible.
-- Added paragraph to discussion comparing our methods of computing the partition functions to alternative methods, e.g., using Hamiltonian methods.

Published as SciPost Phys. 9, 009 (2020)

Reports on this Submission

Anonymous Report 1 on 2020-7-9 (Invited Report)


We thank the authors for considering our comments, and are happy to recommend the manuscript for publication in SciPost.

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