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Fusion of spin fields in W3 conformal field theories

In generic conformal field theories with W3 symmetry, we identify a primary field with rational Kac indices, which produces the full charged and neutral sectors by the fusion processes and , respectively. In this sense, this field generalises the fundamental spin field of the three-state Potts model. Among the degenerate fields produced by these fusions, we single out a ‘parafermion’ field and an ‘energy’ field . In analogy with the Virasoro case, the exact curves for conformal dimensions and are expected to give close estimates for the unitarity bounds in the conformal bootstrap analysis.