$C_2$ Toda theory in the reduced WZNW framework

TL;DR

This paper studies the classical and quantum structure of the $C_2$ Toda theory within the reduced WZNW framework, focusing on the symmetry algebra, representations, and quantization effects on the model's Hilbert space.

Contribution

It provides a detailed analysis of the classical highest weight representations of the $C_2$ $W$ algebra and introduces a quantization scheme that yields new insights into the model's structure.

Findings

Classical highest weight representations of the $C_2$ $W$ algebra are characterized.

Quantization imposes selection rules on the Toda field $u$ and restricts amplitude functions.

Restrictions on the Hilbert space structure of the quantized model are derived.

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.