The Wilson Spool in Locally Flat Spacetimes

TL;DR

This paper defines a Wilson Spool in 3D gravity with zero cosmological constant, based on a one-loop partition function, and discusses its potential generalizations beyond flat backgrounds.

Contribution

It introduces a new, background-independent definition of the Wilson Spool in three-dimensional gravity with vanishing cosmological constant.

Findings

Proposes a Wilson Spool construction from a fixed background holonomy.

Connects the Wilson Spool to one-loop partition functions of spinning fields.

Discusses potential links to 2D versions at non-zero cosmological constant.

Abstract

This paper proposes a definition of what has previously been coined a Wilson Spool in the case of three-dimensional gravity with vanishing cosmological constant. The definition builds upon a construction of the one-loop partition function of a massive, spinning field from a fixed background holonomy. While the background is taken to be a flat-space cosmology, the definition of the Wilson spool is expected to hold independently of the underlying geometry. Some comments are given towards possible connections to its two-dimensional incarnations at non-vanishing cosmological constant.