Accessing Fractional Wilson Lines from U(1) Monodromy Defects on the Fuzzy Sphere
Abstract
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.
Related
- Monodromy Defects of 3D Wilson-Fisher Criticality on the Fuzzy Sphere
- Monodromy line defects on the fuzzy sphere
- Monodromy defects in ABJM theory and integrability
- Conformal data for the O(2) Wilson-Fisher CFT in (2+1)-dimensional spacetime from exact diagonalization and matrix product states on the fuzzy sphere
- Revisiting monodromy defects in O(N) conformal field theories
BibTeX
@misc{tang2026accessing,
title = {{Accessing Fractional Wilson Lines from U(1) Monodromy Defects on the Fuzzy Sphere}},
author = {Yin Tang and W. Zhu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08102},
eprint = {2611.08102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08102},
}
RIS
TY - UNPB
TI - Accessing Fractional Wilson Lines from U(1) Monodromy Defects on the Fuzzy Sphere
AU - Yin Tang
AU - W. Zhu
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08102
UR - https://arxiv.org/abs/2611.08102
AB - 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.
ER -