发表机构
National Center for Theoretical Sciences, National Taiwan University; Institute for Advanced Study, Kyushu University（台湾大学国家理论科学中心; 九州大学高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨广义对称性在无质量重整化群流中的作用，证明幺正极小模型流中未破缺的融合环对称性可稳定红外无隙相，其对应的非简单流结构引发的共振效应或导致相变级联，而对称性可终止这类非常规流。
AI 中文摘要
我们研究了广义对称性在无质量重整化群流或希格斯跃迁中的作用。具体而言，我们重新探讨了幺正极小模型中保持融合环对称性$\text{FR} (SU(2)_{p-2})\nsubseteq \nmathbf{M}(p,p+1)$的无质量重整化群流$\nmathbf{M}(p,p+1) \nrightarrow \noverline{\nmathbf{M}(p-1,p)}$，其中$p$是满足$p>3$的整数。在这一系列流中，我们证明了未破缺的融合环对称性$\text{FR} (SU(2)_{p-2})$消除了$\noverline{\nmathbf{M}(p-1,p)}$模型中的所有相关微扰。因此，红外理论$\noverline{\nmathbf{M}(p-1,p)}$在标度分析层面是稳定的，可被解释为当代理论物理中一种（弱）对称性施加的无隙相。在唯象层面，通过折叠技巧，未破缺的融合环对称性对应一种（半）整数自旋非简单流，这是库珀对的一种变体，涉及由陪集或能级-秩对偶结构产生的非阿贝尔任意子。此外，我们证明了（半）整数自旋非简单流的结构在引发相关微扰和危险无关微扰的共振效应中发挥着核心作用。这种共振效应可能导致相变级联（或系统流向未探索的不动点），而该对称性可以成为这类非常规流的终止器。
英文摘要
We study the role of generalized symmetry in massless renormalization group flows or Higgs transitions. In particular, we revisit the massless renormalization group flows in unitary minimal models, $\mathbf{M}(p,p+1) \rightarrow \overline{\mathbf{M}(p-1,p)}$ preserving the fusion ring symmetry $\text{FR} (SU(2)_{p-2})\subset \mathbf{M}(p,p+1)$ where $p$ is an integer satisfying $p>3$. In this series of flows, we demonstrate that the unbroken fusion ring symmetry $\text{FR} (SU(2)_{p-2})$ eliminates all relevant perturbations in the $\overline{\mathbf{M}(p-1,p)}$ model. Hence, the infrared theory $\overline{\mathbf{M}(p-1,p)}$ is stable at the level of the scaling analysis and can be interpreted as a (weak-)symmetry-enforced gapless phase in contemporary theoretical physics. Phenomenologically, by the folding trick, the unbroken fusion ring symmetry corresponds to a (half-)integer spin nonsimple current, a variant of the Cooper pair involving nonabelian anyons generated from the coset or level-rank duality structures. Moreover, we demonstrate that the structure of (half-)integer spin nonsimple current plays a fundamental role in causing the resonance effect of relevant and dangerously irrelevant perturbations. This resonance effect may result in the cascade of phase transitions (or the system flows to unexplored fixed points), and the symmetry can be a stopper of such unconventional flows.
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