Connecting quasinormal modes and heat kernels in 1-loop determinants

Keeler, Cynthia; Martin, Victoria L.; Svesko, Andrew

doi:10.21468/scipostphys.8.2.017

Cited by 13 publications

(95 citation statements)

References 37 publications

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“…The second subtle point is that similar to the case of rotating BTZ black holes as quotients of H 3 [58], we should require a modified periodicity condition in order that the coordinates are regular for ϕ P r0, 2πs:…”

Section: Classical Contributionmentioning

confidence: 99%

Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization

Nian

Zayas

2020

J. High Energ. Phys.

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We employ supersymmetric localization to determine the exact partition function of 3d N " 2 gauge theories on a background given by a round S 2 fibered over a circle and certain complexified background fields. The Coulomb branch localization locus includes monopole configurations, and the partition function reduces to a matrix model. We consider the partition function of the ABJM theory on this background as an explicit case. We verify that the large-N limit of the ABJM theory partition function produces, in the Cardy limit, the entropy function of the dual rotating, electrically charged asymptotically AdS 4 supersymmetric black holes and thus provides a microscopic explanation for the Bekenstein-Hawking entropy.

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Section: Classical Contributionmentioning

confidence: 99%

Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization

Nian

Zayas

2020

J. High Energ. Phys.

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“…written here as a path integral over all compact Euclidean metrics g. The partition function (1) is interpreted as the norm of the Hartle-Hawking state, i.e., the vacuum state wavefunctional with fixed boundary conditions on a space-like slice [4]. Formally, the full partition function (1) is computed using a saddle point approximation,…”

Section: Introductionmentioning

confidence: 99%

“…where g c are classical solutions to the Euclidean equations of motion, and α is a dimensionless coupling constant equal to the de Sitter radius in Planck units. In the exponential S (i) [g c ] represents the ith quantum correction to the Euclidean action S; S (0) [g c ] is the tree-level contribution, S (1) [g c ] is the 1-loop quantum correction providing information on leading order quantum effects, and so forth.…”

Section: Introductionmentioning

confidence: 99%

“…The first step for de Sitter gravity is straightforward: the infinite set of classical solutions is enumerated by Euclidean dS N , i.e., the sphere S N , and its quotients S N /Γ , for Γ a discrete subgroup of SO(N + 1). The more difficult part of the procedure is carrying out the saddle point approximation (2) in full 1 .…”

Section: Introductionmentioning

confidence: 99%

“…The partition function is therefore typically computed to 1-loop. The leading order quantum correction is given by the 1-loop partition function Z (1) and is given in terms of a collection of functional determinants of kinetic operators. For example, in D-dimensional (Euclidean) de Sitter space Z (1) is given as a ratio of two functional determinants [8,9] Z (1)…”

Section: Introductionmentioning

confidence: 99%

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

Martin

Svesko

2020

SciPost Phys.

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In this note we compute the 1-loop partition function of spin-ss fields on Euclidean de Sitter space S^{2n+1}S2n+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}}LAdS→iLdS, appearing in the dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on thermal \text{AdS}_{2n+1}AdS2n+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}AdS2n+1 can be generalized to calculating 1-loop partition functions on the thermal spherical quotients S^{2n+1}/\mathbb{Z}_{p}S2n+1/ℤp. We further show that the quasinormal mode frequencies encode the group theoretic structure of the spherical spacetimes in question, analogous to the analysis made for thermal AdS in [1-3] .

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A Selberg zeta function for warped AdS3 black holes

Martin

Poddar

2023

J. High Energ. Phys.

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The Selberg zeta function and trace formula are powerful tools used to calculate kinetic operator spectra and quasinormal modes on hyperbolic quotient spacetimes. In this article, we extend this formalism to non-hyperbolic quotients by constructing a Selberg zeta function for warped AdS3 black holes. We also consider the so-called self-dual solutions, which are of interest in connection to near-horizon extremal Kerr. We establish a map between the zeta function zeroes and the quasinormal modes on warped AdS3 black hole backgrounds. In the process, we use a method involving conformal coordinates and the symmetry structure of the scalar Laplacian to construct a warped version of the hyperbolic half-space metric, which to our knowledge is new and may have interesting applications of its own, which we describe. We end by discussing several future directions for this work, such as computing 1-loop determinants (which govern quantum corrections) on the quotient spacetimes we consider, as well as adapting the formalism presented here to more generic orbifolds.

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Connecting quasinormal modes and heat kernels in 1-loop determinants

Cited by 13 publications

References 37 publications

Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization

Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization

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

A Selberg zeta function for warped AdS3 black holes

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