Accessing Fractional Wilson Lines from U(1) Monodromy Defects on the Fuzzy Sphere

Wilson lines are gauge-invariant probes of charge screening and deconfinement, which can detect the response of quantum critical matter to an external charge, but their universal information at strongly-coupled critical points remains hard to access. Here we investigate a continuous family of $U(1)$ monodromy defects of the three-dimensional $O(2)$ Wilson--Fisher conformal field theory, which is dual to fractional Wilson lines in the critical noncompact Abelian Higgs model with one unit-charged scalar. We realize this continuous family of defects within the fuzzy-sphere framework by threading a fractional Aharonov--Bohm flux through the two poles of the sphere. We observe the emergence of charged operators carrying fractional transverse spins, as a characteristic signature of the imposed monodromy. The appearance of displacement operator at its protected dimension supports the conformal nature of this defect line. Crucially, we resolve no relevant symmetry-preserving defect scalar, and identify charge-one monopole operators as relevant symmetry-breaking deformations. Assuming the duality, these results provide non-perturbative evidence that fractional Wilson lines of the critical Abelian Higgs model are stable conformal lines.