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

TL;DR

This paper develops a method to compute the one-loop partition function for arbitrary spin fields on a rotating BTZ background using the Selberg zeta function, extending previous scalar field results to general spins.

Contribution

It generalizes the relation between the Selberg zeta function and one-loop determinants from scalar fields to fields of arbitrary spin on BTZ backgrounds.

Findings

Extended the integer relabeling to general spin fields.

Connected zeros of the Selberg zeta function with poles of the scattering operator.

Discussed the removal of non-square-integrable Euclidean zero modes.

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.