Generalized Toda theories and -algebras associated with integral gradings
(1992) Annals of Physics — Vol. 213, n° 1, p. 1-20 (1992)
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- Abstract
- A general class of conformal Toda theories associated with integral gradings of 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 recover 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.
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Fehér, L., O’Raifeartaigh, L., Ruelle, P., Tsutsui, I., & Wipf, A. (1992). Generalized Toda theories and -algebras associated with integral gradings. Annals of Physics, 213(1), 1-20. https://doi.org/10.1016/0003-4916(92)90280-Y (Original work published 1992)