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Fusion rules and logarithmic representations of a WZW model at fractional level

Matthias R Gaberdiel
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Abstract

The fusion products of admissible representations of the su(2) WZW model at the fractional level k=-4/3 are analysed. It is found that some fusion products define representations for which the spectrum of L_0 is not bounded from below. Furthermore, the fusion products generate representations that are not completely reducible and for which the action of L_0 is not diagonalisable. The complete set of representations that is closed under fusion is identified, and the corresponding fusion rules are derived.

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Matthias R Gaberdiel. 2001-05-11. Fusion rules and logarithmic representations of a WZW model at fractional level. https://doi.org/10.1016/s0550-3213(01)00490-4

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