论文标题
2D CFT中状态的渐近密度，具有不可逆转的对称性
Asymptotic density of states in 2d CFTs with non-invertible symmetries
论文作者
论文摘要
众所周知，有限对称组的$ρ$ $ g $ $ρ$ $ g $与$（\ dimC）^2 $成正比的2D CFT状态的渐近密度。我们展示了当对称性不可固化时如何推广该语句，并由Fusion类别$ \ Mathcal {C} $描述。在此过程中，我们解释了在融合类别对称的情况下，群体表示的作用；这个问题的答案已经在更广泛的数学物理学文献中获得，但在HEP-Th中尚未广为人知。这种理解立即意味着相关函数的选择规则，也使我们能够得出渐近密度。
It is known that the asymptotic density of states of a 2d CFT in an irreducible representation $ρ$ of a finite symmetry group $G$ is proportional to $(\dimρ)^2$. We show how this statement can be generalized when the symmetry can be non-invertible and is described by a fusion category $\mathcal{C}$. Along the way, we explain what plays the role of a representation of a group in the case of a fusion category symmetry; the answer to this question is already available in the broader mathematical physics literature but not yet widely known in hep-th. This understanding immediately implies a selection rule on the correlation functions, and also allows us to derive the asymptotic density.
