Monodromy Defects of 3D Wilson-Fisher Criticality on the Fuzzy Sphere

Abstract

Monodromy (twist) line defects arise as the boundaries of topological symmetry surfaces, which are among the simplest non-trivial conformal defects with direct realizations as magnetic vortex in quantum magnets, as Wilson and t Hooft lines of gauge theories, and as the replica twist operators in quantum information theory. However, their interacting dynamics remains difficult to characterize non-perturbatively. Here we design a way to realize the monodromy boundary conditions in the fuzzy-sphere regularization by threading a symmetry-selective Aharonov-Bohm flux through the two poles of the sphere. We apply this construction to the $\mathbb{Z}_2$ twist of the 3D Ising conformal field theory (CFT), $π$-twist of the 3D O(2) CFT and three inequivalent monodromies of O(3) (centre twist, z-axis $π$-twist and the reflection). For each defect, we extract the low-lying defect spectrum together with bulk-to-defect and defect-defect operator product expansion coefficients, which characterize the operators living on the defect line, their mutual interactions, and how they couple to the surrounding critical bulk. Among the low-lying defect primaries resolved in our spectra, we find no relevant scalar perturbation that preserves all the symmetries of the corresponding defect. The relevant deformations identified in our calculations break at least one preserved symmetry, providing evidence that these monodromy defects are stable against symmetry-preserving relevant perturbations. These results establish a systematic set of non-perturbative conformal data for monodromy defects beyond the Ising twist. Our construction therefore turns the symmetry flux into a tunable knob of the fuzzy-sphere regularization, opening a route to exploring the response of critical matter to distinct defects.