$\mathcal{N}=2$ RG流、非可逆对称性与矩阵分解
$\mathcal{N}=2$ RG flows, Non-Invertible Symmetries and Matrix Factorisations
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中文总结 AI 辅助
该研究通过CFT论证与矩阵分解技术，发现$\mathcal{N}=2$极小模型无质量RG流的拓扑缺陷线无法定义红外对称性，而对应超势切比雪夫形变的有质量可积流的缺陷可一致形变并定义对称性。
中文摘要 AI 辅助
我们研究第k个$\mathcal{N}=2$极小模型的拓扑缺陷线在一阶最不相关微扰下的保留情况。通常认为这些缺陷线应定义红外理论的对称性，对于常规“无质量”流，该对称性对应第(k-2)个$\mathcal{N}=2$极小模型。我们利用共形场论（CFT）论证表明这并不成立，还通过矩阵分解技术重现了该结果：尽管对应的B型缺陷可在微扰一阶调整，但二阶存在与超对称反常相关的阻碍。相比之下，对于对应超势切比雪夫形变的相关有质量可积流，所有这些缺陷均可一致形变，且确实定义了有质量红外理论的对称性。
英文摘要
We study the behaviour of the topological defect lines of the $k^{\rm th}$ ${\cal N}=2$ minimal models that are preserved by the least relevant perturbation to first order. It is usually believed that these defects should then also define symmetries of the IR theory, which for the usual "massless'' flow should be the $(k-2)^{\rm nd}$ ${\cal N}=2$ minimal model. Using CFT arguments we show that this is not possible. We also reproduce this result using matrix factorisation techniques: while the corresponding B-type defects can be adjusted to first order in the deformation, there is an obstruction at second order, which is associated with a supersymmetry anomaly. By contrast, for the associated massive integrable flow, which corresponds to a Chebyshev deformation of the superpotential, all of these defects can be consistently deformed, and they indeed define symmetries of the massive IR theory.
