发表机构
Fudan University; Hong Kong University of Science and Technology; Hunan University; Hefei National Laboratory; Westlake Institute for Advanced Study; Westlake University（复旦大学; 香港科技大学; 湖南大学; 合肥国家实验室; 西湖高等研究院; 西湖大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究嵌入三维$O(N)$临界体的线缺陷，用模糊球技术证明稳定缺陷共形不动点存在，发现$N<3$时无法支撑对称性破缺缺陷，$N\rtrapprox3$时可行。
AI 中文摘要
对于具有短程相互作用的一维经典系统，离散对称性的自发破缺是不存在的，但嵌入体临界性中的线缺陷被期望表现出稳定的离散对称性自发破缺。在此，我们研究了浸没于三维体中的钉扎场线缺陷的行为，该三维体被调谐至$O(N)$威尔逊-费舍尔临界点。借助模糊球技术，我们为稳定缺陷共形不动点的存在提供了令人信服的证据，并通过$g$函数证明不存在相关算符且自由度少于体不动点，从而论证了其重整化群稳定性。此外，我们针对不同$N$研究了缺陷畴壁算符，确定其在$N\rtrapprox3$时为无关算符，而在$N<3$时为相关算符。这些证据表明，对于$N<3$的威尔逊-费舍尔普适类，与临界体耦合的一维缺陷因畴壁增殖无法支撑稳定的对称性自发破缺缺陷不动点；而在$N\rtrapprox3$的情况下，对称性破缺缺陷是可能存在的。
英文摘要
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 $N\gtrsim 3$ 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 $N \gtrsim 3$ a symmetry broken defect is possible.
