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arXiv · 1906.01323

Fusion of spin fields in $W_3$ conformal field theories

Yacine Ikhlef·Hirohiko Shimada
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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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Yacine Ikhlef, Hirohiko Shimada. 2019-06-04. Fusion of spin fields in $W_3$ conformal field theories. https://doi.org/10.1088/1751-8121/ab56e3

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