Symmetry-breaking line defects embedded to a 3D O(N) critical bulk
Abstract
While spontaneous breaking of a discrete symmetry in one-dimensional classical systems with short-range interactions is absent, it is expected that a line defect embedded in a bulk criticality exhibits a stable discrete symmetry spontaneous breaking. Here, we investigate the behavior of a pinning-field line defect immersed in a 3D bulk that remains tuned to the O(N) Wilson-Fisher critical point. Employing the fuzzy sphere technique, we provide convincing evidence of the existence of stable defect conformal fixed points, and we demonstrate their renormalization group stability by showing no relevant operator and less effective degrees of freedom than that at bulk fixed point via g-function. Moreover, we investigate the defect domain wall operator for various N, and we identify that it becomes irrelevance for N≳ 3 but it is relevant for N<3.These evidence indicate that a one-dimensional defect coupled to a critical bulk cannot support a stable symmetry spontaneously broken defect fixed point due to domain wall proliferation for N<3 Wilson-Fisher universality, while in the case of N ≳ 3 a symmetry broken defect is possible.
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BibTeX
@misc{yang2026symmetrybreaking,
title = {{Symmetry-breaking line defects embedded to a 3D $O(N)$ critical bulk}},
author = {Shuai Yang and Liang-dong Hu and Yan Chen and W. Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03289},
eprint = {2609.03289},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03289},
}
RIS
TY - UNPB
TI - Symmetry-breaking line defects embedded to a 3D O(N) critical bulk
AU - Shuai Yang
AU - Liang-dong Hu
AU - Yan Chen
AU - W. Zhu
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03289
UR - https://arxiv.org/abs/2609.03289
AB - While spontaneous breaking of a discrete symmetry in one-dimensional classical systems with short-range interactions is absent, it is expected that a line defect embedded in a bulk criticality exhibits a stable discrete symmetry spontaneous breaking. Here, we investigate the behavior of a pinning-field line defect immersed in a 3D bulk that remains tuned to the O(N) Wilson-Fisher critical point. Employing the fuzzy sphere technique, we provide convincing evidence of the existence of stable defect conformal fixed points, and we demonstrate their renormalization group stability by showing no relevant operator and less effective degrees of freedom than that at bulk fixed point via g-function. Moreover, we investigate the defect domain wall operator for various N, and we identify that it becomes irrelevance for N≳ 3 but it is relevant for N<3.These evidence indicate that a one-dimensional defect coupled to a critical bulk cannot support a stable symmetry spontaneously broken defect fixed point due to domain wall proliferation for N<3 Wilson-Fisher universality, while in the case of N ≳ 3 a symmetry broken defect is possible.
ER -