BTZ one-loop determinants via the Selberg zeta function for general spin

Abstract

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 function associated with ${\mathbb{H}}^3/\mathbb{Z}$, extending (1811.08433). Previously, Perry and Williams showed for a scalar field that the zeros of the Selberg zeta function coincide with the poles of the associated scattering operator upon a relabeling of integers. We extend the integer relabeling to the case of general spin, and discuss its relationship to the removal of non-square-integrable Euclidean zero modes.