### Abstract

A new formulation of Toda theories is proposed by showing that they can be regarded as certain gauged Wess-Zumino-Novikov-Witten (WZNW) models. It is argued that the WZNW variables are the proper ones for Toda theory, since all the physically permitted Toda solutions are regular when expressed in these variables. A detailed study of classical Toda theories and their W-algebras is carried out from this unified WZNW point of view. We construct a primary field basis for the W-algebra for any group, we obtain a new method for calculating the W-algebra and its action on the Toda fields by constructing its Kac-Moody implementation, and we analyse the relationship between W-algebras and Casimir algebras. The W-algebra of G_{2} and the Casimir algebras for the classical groups are exhibited explicitly.

Original language | English |
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Pages (from-to) | 76-136 |

Number of pages | 61 |

Journal | Annals of Physics |

Volume | 203 |

Issue number | 1 |

DOIs | |

Publication status | Published - Oct 1990 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Annals of Physics*,

*203*(1), 76-136. https://doi.org/10.1016/0003-4916(90)90029-N