The Wilson Spool in Locally Flat Spacetimes

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.