探索 $c=2$ 时的对偶对称性、多临界点与重整化群流
Exploring duality symmetries, multicriticality and RG flows at $c = 2$
AI总结：
本文在 $c=2$ 共形流形上系统构造非可逆对偶缺陷，分析多临界点的范畴数据与缺陷 Hilbert 空间，并阐明其对 RG 流红外端的约束。
摘要：
在本工作中，我们研究了沿 $c=2$ 共形流形的环面分支上非可逆对偶对称性的实现。我们实施了一套构造对称性缺陷的系统程序，以表明沿该分支的所有有理共形场论都具有对偶对称性。此外，我们深入分析了两个具有代表性的多临界理论案例，即环面分支与各种轨形分支相交之处。对于这些特定例子，我们借助模协变性获得了与对偶对称性相关的范畴数据和缺陷 Hilbert 空间。最后，我们研究了这些新颖对称性与各种恰好边缘及相关形变之间的相互作用，包括若干具有代表性的重整化群流例子，在这些流中，红外区受到非可逆对称性及其反常的约束。
英文摘要：
In this work, we study the realization of non-invertible duality symmetries along the toroidal branch of the $c=2$ conformal manifold. A systematic procedure to construct symmetry defects is implemented to show that all Rational Conformal Field Theories along this branch enjoy duality symmetries. Furthermore, we delve into an in-depth analysis of two representative cases of multicritical theories, were the toroidal branch meets various orbifold branches. For these particular examples, the categorical data and the defect Hilbert spaces associated to the duality symmetries are obtained by resorting to modular covariance. Finally, we study the interplay between these novel symmetries and the various exactly marginal and relevant deformations, including some representative examples of Renormalization Group flows where the infrared is constrained by the non-invertible symmetries and their anomalies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
