Hu Liangdong, He Yin-Chen, Zhu W
Department of Physics, School of Science, Westlake University, Hangzhou, 310030, PR China.
Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou, 310024, PR China.
Nat Commun. 2024 Apr 30;15(1):3659. doi: 10.1038/s41467-024-47978-y.
Defects in conformal field theory (CFT) are of significant theoretical and experimental importance. The presence of defects theoretically enriches the structure of the CFT, but at the same time, it makes it more challenging to study, especially in dimensions higher than two. Here, we demonstrate that the recently-developed theoretical scheme, fuzzy (non-commutative) sphere regularization, provides a powerful lens through which one can dissect the defect of 3D CFTs in a transparent way. As a notable example, we study the magnetic line defect of 3D Ising CFT and clearly demonstrate that it flows to a conformal defect fixed point. We have identified 6 low-lying defect primary operators, including the displacement operator, and accurately extract their scaling dimensions through the state-operator correspondence. Moreover, we also compute one-point bulk correlators and two-point bulk-defect correlators, which show great agreement with predictions of defect conformal symmetry, and from which we extract various bulk-defect operator product expansion coefficients. Our work demonstrates that the fuzzy sphere offers a powerful tool for exploring the rich physics in 3D defect CFTs.
共形场论（CFT）中的缺陷具有重要的理论和实验意义。从理论上讲，缺陷的存在丰富了CFT的结构，但与此同时，这也使得研究更具挑战性，尤其是在高于二维的维度中。在此，我们证明，最近发展的理论方案，即模糊（非对易）球面正则化，提供了一个强大的视角，通过它可以以一种清晰的方式剖析三维共形场论中的缺陷。作为一个显著的例子，我们研究了三维伊辛共形场论的磁线缺陷，并清楚地证明它流向一个共形缺陷不动点。我们确定了6个低能缺陷原初算符，包括位移算符，并通过态-算符对应精确提取了它们的标度维数。此外，我们还计算了体单点关联函数和体-缺陷两点关联函数，它们与缺陷共形对称性的预测高度吻合，并且从中我们提取了各种体-缺陷算符乘积展开系数。我们的工作表明，模糊球面为探索三维缺陷共形场论中的丰富物理提供了一个强大的工具。
