1. Asymptotic density of states in 2d CFTs with non-invertible symmetries.
- Author
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Lin, Ying-Hsuan, Okada, Masaki, Seifnashri, Sahand, and Tachikawa, Yuji
- Subjects
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DENSITY of states , *MATHEMATICAL physics , *FINITE groups , *SYMMETRY groups , *SYMMETRY - Abstract
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 (dim ρ)2. We show how this statement can be generalized when the symmetry can be non-invertible and is described by a fusion category 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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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