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The CFT of the $\mathrm{SU}(N)$ level $k$ Kac-Moody current algebra has many Kac-Moody primary fields. I wonder if any one has calculated the quantum dimensions of those Kac-Moody primary fields.

I know that, for $\mathrm{SU}(2)$ level $k$ Kac-Moody current algebra, there is a general expression for the quantum dimensions of the $\mathrm{SU}(2)$ primary fields.

Qmechanic
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Xiao-Gang Wen
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2 Answers2

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I found a nice data base on Web. For example https://www.math.ksu.edu/~gerald/voas/mtc/kmA3_3.html list the data for SU(4) level 3 case.

Xiao-Gang Wen
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The S matrix of affine Lie algebra can be calculated by the Kac-Peterson formula, which can also be found in Theorem 13.8 in Kac's book.

Ce Shen
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