Normal modes in thermal AdS via the Selberg zeta function

Martin, Victoria; Svesko, Andrew

doi:10.21468/SciPostPhys.9.1.009

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.

View Journal Article

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0018330

OSTI ID:: 1640231

Alternate ID(s):: OSTI ID: 1803365

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

Publisher:: Stichting SciPostCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (25)

The spinor heat kernel in maximally symmetric spaces Camporesi, Roberto Communications in Mathematical Physics, Vol. 148, Issue 2 https://doi.org/10.1007/BF02100862	journal	August 1992
Logarithmic corrections to extremal black hole entropy from quantum entropy function Banerjee, Shamik; Gupta, Rajesh K.; Sen, Ashoke Journal of High Energy Physics, Vol. 2011, Issue 3 https://doi.org/10.1007/JHEP03(2011)147	journal	March 2011
Higher spin quasinormal modes and one-loop determinants in the BTZ black hole Datta, Shouvik; David, Justin R. Journal of High Energy Physics, Vol. 2012, Issue 3 https://doi.org/10.1007/JHEP03(2012)079	journal	March 2012
The heat kernel on AdS 3 and its applications David, Justin R.; Gaberdiel, Matthias R.; Gopakumar, Rajesh Journal of High Energy Physics, Vol. 2010, Issue 4 https://doi.org/10.1007/JHEP04(2010)125	journal	April 2010
Partition functions for higher-spin theories in AdS Gupta, Rajesh Kumar; Lal, Shailesh Journal of High Energy Physics, Vol. 2012, Issue 7 https://doi.org/10.1007/JHEP07(2012)071	journal	July 2012
Holographic entanglement beyond classical gravity Barrella, Taylor; Dong, Xi; Hartnoll, Sean A. Journal of High Energy Physics, Vol. 2013, Issue 9 https://doi.org/10.1007/JHEP09(2013)109	journal	September 2013
Tweaking one-loop determinants in AdS3 Castro, Alejandra; Keeler, Cynthia; Szepietowski, Phillip Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/JHEP10(2017)070	journal	October 2017
The heat kernel on AdS Gopakumar, Rajesh; Gupta, Rajesh Kumar; Lal, Shailesh Journal of High Energy Physics, Vol. 2011, Issue 11 https://doi.org/10.1007/JHEP11(2011)010	journal	November 2011
Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates Sen, Ashoke General Relativity and Gravitation, Vol. 44, Issue 5 https://doi.org/10.1007/s10714-012-1336-5	journal	February 2012
Harmonic analysis and propagators on homogeneous spaces Camporesi, Roberto Physics Reports, Vol. 196, Issue 1-2 https://doi.org/10.1016/0370-1573(90)90120-Q	journal	November 1990
On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces Camporesi, Roberto; Higuchi, Atsushi Journal of Geometry and Physics, Vol. 20, Issue 1 https://doi.org/10.1016/0393-0440(95)00042-9	journal	September 1996
Large N field theories, string theory and gravity Aharony, Ofer; Gubser, Steven S.; Maldacena, Juan Physics Reports, Vol. 323, Issue 3-4 https://doi.org/10.1016/S0370-1573(99)00083-6	journal	January 2000
Heat kernel expansion: user's manual Vassilevich, D. V. Physics Reports, Vol. 388, Issue 5-6 https://doi.org/10.1016/j.physrep.2003.09.002	journal	December 2003
Symmetric tensor spherical harmonics on the N ‐sphere and their application to the de Sitter group SO( N ,1) Higuchi, Atsushi Journal of Mathematical Physics, Vol. 28, Issue 7 https://doi.org/10.1063/1.527513	journal	July 1987
Spectral functions and zeta functions in hyperbolic spaces Camporesi, Roberto; Higuchi, Atsushi Journal of Mathematical Physics, Vol. 35, Issue 8 https://doi.org/10.1063/1.530850	journal	August 1994
The (2 + 1)-dimensional black hole Carlip, S. Classical and Quantum Gravity, Vol. 12, Issue 12 https://doi.org/10.1088/0264-9381/12/12/005	journal	December 1995
Black hole determinants and quasinormal modes Denef, Frederik; Hartnoll, Sean A.; Sachdev, Subir Classical and Quantum Gravity, Vol. 27, Issue 12 https://doi.org/10.1088/0264-9381/27/12/125001	journal	April 2010
One-loop partition functions of 3D gravity Giombi, Simone; Maloney, Alexander; Yin, Xi Journal of High Energy Physics, Vol. 2008, Issue 08 https://doi.org/10.1088/1126-6708/2008/08/007	journal	August 2008
Functional determinants, generalized BTZ geometries and Selberg zeta function Aros, R.; Díaz, D. E. Journal of Physics A: Mathematical and Theoretical, Vol. 43, Issue 20 https://doi.org/10.1088/1751-8113/43/20/205402	journal	April 2010
Partition functions, the Bekenstein bound and temperature inversion in anti-de Sitter space and its conformal boundary Gibbons, G. W.; Perry, M. J.; Pope, C. N. Physical Review D, Vol. 74, Issue 8 https://doi.org/10.1103/PhysRevD.74.084009	journal	October 2006
Quantum oscillations and black hole ringing Denef, Frederik; Hartnoll, Sean A.; Sachdev, Subir Physical Review D, Vol. 80, Issue 12 https://doi.org/10.1103/PhysRevD.80.126016	journal	December 2009
Black hole in three-dimensional spacetime Bañados, Máximo; Teitelboim, Claudio; Zanelli, Jorge Physical Review Letters, Vol. 69, Issue 13 https://doi.org/10.1103/PhysRevLett.69.1849	journal	September 1992
QUANTUM ENTROPY FUNCTION FROM AdS ₂ / CFT ₁ CORRESPONDENCE Sen, Ashoke International Journal of Modern Physics A, Vol. 24, Issue 23 https://doi.org/10.1142/S0217751X09045893	journal	September 2009
Connecting quasinormal modes and heat kernels in 1-loop determinants Keeler, Cynthia; Martin, Victoria; Svesko, Andrew SciPost Physics, Vol. 8, Issue 2 https://doi.org/10.21468/SciPostPhys.8.2.017	journal	January 2020
Zeta Function Expression of Spin Partition Functions on Thermal AdS3 L. Williams, Floyd Mathematics, Vol. 3, Issue 3 https://doi.org/10.3390/math3030653	journal	July 2015

Similar Records

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

Journal Article · Mon Sep 14 00:00:00 EDT 2020 · SciPost Physics · OSTI ID:1660308

String correlators on $\text{AdS}_3$: Analytic structure and dual CFT

Journal Article · Tue Sep 06 00:00:00 EDT 2022 · SciPost Physics · OSTI ID:1885621

Normal modes in thermal AdS via the Selberg zeta function

Citation Formats

References (25)

Similar Records

Related Subjects