Normal modes in thermal AdS via the Selberg zeta function

Martin, Victoria; Svesko, Andrew

doi:10.21468/SciPostPhys.9.1.009

Title: Normal modes in thermal AdS via the Selberg zeta function

Journal Article · Tue Jul 21 00:00:00 EDT 2020 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.9.1.009· OSTI ID:1640231

Martin, Victoria ^[1]; Svesko, Andrew ^[1]

Arizona State University

The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin s $s$ fields on hyperbolic quotient spacetimes \mathbb{H}^{3}/\mathbb{Z} $ℍ^{3} / ℤ$ are related via the Selberg zeta function. We extend that analysis to thermal \text{AdS}_{2n+1} ${AdS}_{2 n + 1}$ backgrounds, with quotient structure \mathbb{H}^{2n+1}/\mathbb{Z} $ℍ^{2 n + 1} / ℤ$ . 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.

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Research Organization:: Arizona State Univ., Tempe, AZ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0018330

OSTI ID:: 1640231

Alternate ID(s):: OSTI ID: 1803365

Journal Information:: SciPost Physics, Journal Name: SciPost Physics Vol. 9 Journal Issue: 1; ISSN 2542-4653

Publisher:: Stichting SciPostCopyright Statement

Country of Publication:: Netherlands

Language:: English

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Cited by: 3 works

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