Massive fields and Wilson spools in JT gravity

We give a prescription for minimally coupling massive matter to JT gravity with either sign of cosmological constant directly in its formulation as a topological BF theory. This coupling takes the form of a ‘Wilson spool,’ originally introduced in the context of three-dimensional gravity. The Wilson spool expresses the exact one-loop partition function as the integral over a Wilson loop operator. We construct the spool by considering the partition function of a massive scalar field on Euclidean dS _2 2 and on Euclidean AdS _2 2 . We discuss its extension to other geometries (including the ‘trumpet’ and conical defect geometries) and its relation to the three-dimensional spool through dimensional reduction.