Symmetry reduction of Wilson loop operators in Chern–Simons theory

Develop a concrete method to perform symmetry reductions of Wilson loop operators in Euclidean Chern–Simons gauge theories and determine the corresponding observables in the lower‑dimensional theories obtained by spherical symmetry reduction, so that the semiclassical comparison extends beyond the identity observable (the partition function).

Background

The paper establishes semiclassical agreement between certain Chern–Simons theories and their symmetry‑reduced lower‑dimensional counterparts at the level of the partition function, using spherical symmetry reductions. However, while the partition function (identity observable) is analyzed, the authors note the absence of a method to handle symmetry reduction for Wilson loop operators, which are the central gauge‑invariant observables in Chern–Simons theory.

This gap prevents extending the semiclassical correspondence to the full set of observables. The authors therefore explicitly flag the development of a technology for reducing Wilson loops—and identifying their images in the reduced theory—as an open problem.