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

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.

Note:

36 pages harvmac (b), 4 figures; references added Report-no: KCL-MTH-01-10 Subj-class: High Energy Physics - Theory; Quantum Algebra

11.25.Hf
Wess-Zumino-Witten model: SU(2)
algebra: fusion
algebra: affine
algebra: representation
field theory: conformal
S-matrix
bibliography

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Figures(0)

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