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

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 L0 is not bounded from below. Furthermore, the fusion products generate representations that are not completely reducible and for which the action of L0 is not diagonalisable. The complete set of representations that is closed under fusion is identified, and the corresponding fusion rules are derived.