# Fusion of spin fields in $W_3$ conformal field theories

Abstract : In generic conformal field theories with W 3 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.
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https://hal.archives-ouvertes.fr/hal-02166555
Contributor : Inspire Hep <>
Submitted on : Thursday, June 27, 2019 - 12:02:59 AM
Last modification on : Wednesday, November 25, 2020 - 3:57:13 AM

### Citation

Yacine Ikhlef, Hirohiko Shimada. Fusion of spin fields in $W_3$ conformal field theories. J.Phys.A, 2020, 53 (1), pp.015203. ⟨10.1088/1751-8121/ab56e3⟩. ⟨hal-02166555⟩

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