Abstract

Three-dimensional gravity, having no propagating degrees of freedom, shares many features with topological field theory. Correspondingly, Chern-Simons (CS) theory provides an attractive framework for quantizing 3d gravity, at least around a fixed saddle-point. But how do we describe matter in CS gravity while retaining its useful features? In this talk I will focus on the CS description of Euclidean de Sitter space about its three-sphere saddle. I will construct a gauge-invariant object corresponding to the quantum-gravity corrected one-loop determinant of a scalar field. This object, which we coin the “Wilson spool,” can be interpreted as a collection of Wilson loops winding arbitrarily many times around the three-sphere. Constructing and, subsequently, evaluating the spool will require us to revisit starting assumptions about unitarity of the representations appearing in the Wilson loops as well as the library of “exact methods” available to CS theories on the three-sphere. The result will be an object that reduces to the scalar one-loop determinant on a three-sphere in the limit that Newton’s constant vanishes yet can be evaluated at in any order in G_N perturbation theory. Time (and attention) remaining, I will either discuss potential further applications of the Wilson spool (either to spinning fields or to contexts outside of de Sitter) or ramble about my confusions regarding “edge modes” in this theory.