# 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 $\sigma$ with rational Kac indices, which produces the full $\mathbb{Z}_3$ charged and neutral sectors by the fusion processes $\sigma \times \sigma$ and $\sigma \times \sigma^*$, respectively. In this sense, this field generalises the $\mathbb{Z}_3$ fundamental spin field of the three-state Potts model. Among the degenerate fields produced by these fusions, we single out a parafermion' field $\psi$ and an energy' field $\varepsilon$. In analogy with the Virasoro case, the exact curves for conformal dimensions $(h_\sigma,h_\psi)$ and $(h_\sigma,h_\varepsilon)$ 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, August 14, 2019 - 10:50:45 PM

### Citation

Yacine Ikhlef, Hirohiko Shimada. Fusion of spin fields in $W_3$ conformal field theories. 2019. ⟨hal-02166555⟩

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