### 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 |
---|---|

Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Annals of Physics |

Volume | 213 |

Issue number | 1 |

DOIs | |

Publication status | Published - 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

**Generalized Toda theories and W-algebras associated with integral gradings.** / Fehér, L.; O'Raifeartaigh, L.; Ruelle, P.; Tsutsui, I.; Wipf, A.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 213, no. 1, pp. 1-20. https://doi.org/10.1016/0003-4916(92)90280-Y

}

TY - JOUR

T1 - Generalized Toda theories and W-algebras associated with integral gradings

AU - Fehér, L.

AU - O'Raifeartaigh, L.

AU - Ruelle, P.

AU - Tsutsui, I.

AU - Wipf, A.

PY - 1992

Y1 - 1992

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0010054571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010054571&partnerID=8YFLogxK

U2 - 10.1016/0003-4916(92)90280-Y

DO - 10.1016/0003-4916(92)90280-Y

M3 - Article

AN - SCOPUS:0010054571

VL - 213

SP - 1

EP - 20

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 1

ER -