Connecting quasinormal modes and heat kernels in 1-loop determinants

  title={Connecting quasinormal modes and heat kernels in 1-loop determinants},
  author={Cynthia A. Keeler and Victoria L. Martin and Andrew Svesko},
  journal={arXiv: High Energy Physics - Theory},
We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode… Expand
6 Citations

Tables from this paper

Black hole one-loop determinants in the large dimension limit
We calculate the contributions to the one-loop determinant for transverse traceless gravitons in an n + 3-dimensional Schwarzschild black hole background in the large dimension limit, due to the SO(Expand
Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization
We employ supersymmetric localization to determine the exact partition function of 3d $\mathcal{N}=2$ gauge theories on a background given by a round $S^2$ fibered over a circle and certainExpand
Emergence of Spacetime: From Entanglement to Einstein
Here I develop the connection between thermodynamics, entanglement, and gravity. I begin by showing that the classical null energy condition (NEC) can arise as a consequence of the second law ofExpand
Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity
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 modeExpand
BTZ one-loop determinants via the Selberg zeta function for general spin
We relate the heat kernel and quasinormal mode methods of computing the 1-loop partition function of arbitrary spin fields on a rotating (Euclidean) BTZ background using the Selberg zeta functionExpand
Normal modes in thermal AdS via the Selberg zeta function
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 zetaExpand


Higher spin quasinormal modes and one-loop determinants in the BTZ black hole
A bstractWe solve the wave equations of arbitrary integer spin fields in the BTZ black hole background and obtain exact expressions for their quasinormal modes. We show that these quasinormal modesExpand
The heat kernel on AdS3 and its applications
We derive the heat kernel for arbitrary tensor fields on S3 and (Euclidean) AdS3 using a group theoretic approach. We use these results to also obtain the heat kernel on certain quotients of theseExpand
Heat kernel expansion: user's manual
Abstract The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect usefulExpand
Tweaking one-loop determinants in AdS3
A bstractWe revisit the subject of one-loop determinants in AdS3 gravity via the quasi-normal mode method. Our goal is to evaluate a one-loop determinant with chiral boundary conditions for theExpand
Zeta function regularization of path integrals in curved spacetime
This paper describes a technique for regularizing quadratic path integrals on a curved background spacetime. One forms a generalized zeta function from the eigenvalues of the differential operatorExpand
Functional determinants, generalized BTZ geometries and Selberg zeta function
We continue the study of a special entry in the AdS/CFT dictionary, namely a holographic formula relating the functional determinant of the scattering operator in an asymptotically locally anti-deExpand
Can one hear the Riemann zeros in black hole ringing
We elaborate on an entry of the AdS/CFT dictionary relating functional determinants: the determinant of the one-loop contribution to the effective gravitational action by bulk scalars in anExpand
Holographic formula for the determinant of the scattering operator in thermal AdS
A 'holographic formula' expressing the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter (ALAdS) space has been proposed in terms of a relative functionalExpand
One-loop Partition Functions of 3D Gravity
We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and gravitonExpand
Quantum fields and extended objects in space-times with constant curvature spatial section
Abstract The heat-kernel expansion and ζ-regularization techniques for quantum field theory and extended objects on curved space-times are reviewed. In particular, ultrastatic space-times withExpand