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What are the quantum dimensions of the primary fields for SU(N) level k Kac-Moody current algebras?

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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.

This post imported from StackExchange Physics at 2015-05-30 00:18 (UTC), posted by SE-user Xiao-Gang Wen
asked May 27, 2015 in Theoretical Physics by Xiao-Gang Wen (3,319 points) [ no revision ]
Maybe nikhef.nl/~t58/Site/Kac.html this could be helpful. It gives pretty much everything one needs to know about WZW CFTs, although not fully analytically.

This post imported from StackExchange Physics at 2015-05-30 00:18 (UTC), posted by SE-user Meng Cheng
Note: Also posted to MO.

This post imported from StackExchange Physics at 2015-05-30 00:18 (UTC), posted by SE-user ACuriousMind

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