$C_2$ Toda theory in the reduced WZNW framework

Abstract

We consider the $C_2$ Toda theory in the reduced WZNW framework. Analysing the classical representation space of the symmetry algebra (which is the corresponding $C_2$ $W$ algebra) we determine its classical highest weight representations. We quantise the model promoting only the relevant quantities to operators. Using the quantised equation of motion we determine the selection rules for the $u$ field that corresponds to one of the Toda fields and give restrictions for its amplitude functions and for the structure of the Hilbert space of the model.

26 pages, TeX, ITP Budapest 501, minor modifications

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