Spinning up the spool: Massive spinning fields in 3d quantum gravity

TL;DR

This paper introduces a method to include massive spinning fields in 3D quantum gravity's path integral using a Wilson spool, providing new insights and explicit calculations in specific backgrounds.

Contribution

It develops a group-theoretic derivation of the Wilson spool for coupling spinning fields, extending previous proposals and enabling explicit quantum correction calculations.

Findings

Successful incorporation of massive spinning fields via Wilson spool

Explicit quantum corrections on S^3 background

Renormalization of G_N and mass at leading order

Abstract

We show how to incorporate massive spinning fields into the Euclidean path integral of three-dimensional quantum gravity via its Chern-Simons formulation. The coupling of the spinning fields to gravity is captured by a Wilson spool, a collection of Wilson loops winding around closed paths of the geometry, and generalizes the proposal of [1,2]. We present a robust derivation of the Wilson spool by providing a new group-theoretic perspective of the quasinormal mode method for one-loop determinants. We test our proposal on Euclidean BTZ and $S^3$ backgrounds. We also evaluate explicitly the quantum corrections to the path integral on $S^3$, and report on how $G_N$ and the mass are renormalized to leading order in perturbation theory.