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arXiv · 2208.05495

Asymptotic density of states in 2d CFTs with non-invertible symmetries

Ying-Hsuan Lin·Masaki Okada·Sahand Seifnashri·Yuji Tachikawa
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Abstract

It is known that the asymptotic density of states of a 2d CFT in an irreducible representation $\rho$ of a finite symmetry group $G$ is proportional to $(\dim\rho)^2$. 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.

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Ying-Hsuan Lin, Masaki Okada, Sahand Seifnashri, Yuji Tachikawa. 2022-08-10. Asymptotic density of states in 2d CFTs with non-invertible symmetries. https://doi.org/10.1007/jhep03(2023)094

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