### Abstract

A general class of conformal Toda theories associated with integral gradings of the simple Lie algebras is investigated. These generalized Toda theories are obtained by reducing the Wess-Zumino-Novikov-Witten (WZNW) theory by first class constraints, and thus they inherite extended conformal symmetry algebras, generalized W-algebras, and current dependent Kac-Moody (KM) symmetries from the WZNW theory, which are analysed in detail in a non-degenerate case. We uncover an sl(2) structure underlying the generalized W-algebras, which allows for identifying the primary fields, and give a simple algorithm for implementing the W-symmetries by current dependent KM transformations, which can be used to compute the action of the W-algebra on any quantity. We establish how the Lax pair of Toda theory arises in the WZNW framework and show that a recent result of Mansfield and Spence, which interprets the W-symmetry of the Toda theory by means of non-Abelian form preserving gauge transformations of the Lax pair, arises immediately as a consequence of the KM interpretation.

Original language | English |
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Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Annals of Physics |

Volume | 213 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1992 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*213*(1), 1-20. https://doi.org/10.1016/0003-4916(92)90280-Y