Abstract
Using the FS and HST versions of the free N = 4 matter multiplet (O4, (1/2)4), we construct two N = 4 SU(2) conformal superfield models. The corresponding N = 4 conserved currents are given. We find that no N = 4 SU(2) Liouville model exists as long as the SU(2) KM symmetry is manifestly preserved. However allowing an explicit breaking of the SU(2) KM subsymmetry of the N = 4 conformal algebra down to U(1) KM, we obtain a Feigin–Fuchs extension of the N = 4 supercurrent showing that N = 4 Liouville theory and its Toda generalizations could exist. Quantization and the N = 4 conformal anomaly are studied.
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