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

Authors
Publication Date
Jun 27, 2019
Source
HAL-INRIA
Keywords
Language
English
License
Unknown
External links

## 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.

Seen <100 times