Normal modes in thermal AdS via the Selberg zeta function

Abstract

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.

arXiv comment22 pages, clarifications added, Scipost formatting

References in corpus (20)

• Large N Field Theories, String Theory and Gravity
• The Black Hole in Three Dimensional Space Time
• Heat kernel expansion: user's manual
• The (2+1)-Dimensional Black Hole
• On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• One-loop Partition Functions of 3D Gravity
• Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
• Holographic entanglement beyond classical gravity
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Quantum oscillations and black hole ringing
• Black hole determinants and quasinormal modes
• The Heat Kernel on AdS_3 and its Applications
• The Heat Kernel on $AdS$
• Tweaking one-loop determinants in AdS${}_3$
• Partition Functions for Higher-Spin theories in AdS
• Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary
• Higher spin quasinormal modes and one-loop determinants in the BTZ black hole
• Connecting quasinormal modes and heat kernels in 1-loop determinants
• Functional determinants, generalized BTZ geometries and Selberg zeta function

Cited by in corpus (4)

• On partition functions and phases of scalars in AdS
• Phases of theories with fermions in AdS
• Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity
• Partition functions for $U(1)$ vectors and phases of scalar QED in AdS