Kavli Affiliate: Yuji Tachikawa
| First 5 Authors: Ying-Hsuan Lin, Masaki Okada, Sahand Seifnashri, Yuji Tachikawa,
| Summary:
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 $(dimrho)^2$. 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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