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 ss fields on hyperbolic quotient spacetimes \mathbb{H}^{3}/\mathbb{Z}ℍ3/ℤ are related via the Selberg zeta function. We extend that analysis to thermal \text{AdS}_{2n+1}AdS2n+1 backgrounds, with quotient structure \mathbb{H}^{2n+1}/\mathbb{Z}ℍ2n+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.