Global Aspects of the WZNW Reduction to Toda Theories

Details Global Aspects of the WZNW Reduction to Toda Theories Global Aspects of the WZNW Reduction to Toda Theories

1994-08-11

arxiv.org/abs/hep-th/9408065v1

Prog.Theor.Phys.Suppl.118:173-190,1995

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, INS-Rep.-1048

Scientific paper

10.1143/PTPS.118.173

It is well-known that the Toda Theories can be obtained by reduction from the Wess-Zumino-Novikov-Witten (WZNW) model, but it is less known that this WZNW $\rightarrow$ Toda reduction is \lq incomplete'. The reason for this incompleteness being that the Gauss decomposition used to define the Toda fields from the WZNW field is valid locally but not globally over the WZNW group manifold, which implies that actually the reduced system is not just the Toda theory but has much richer structures. In this note we furnish a framework which allows us to study the reduced system globally, and thereby present some preliminary results on the global aspects. For simplicity, we analyze primarily 0 $+$ 1 dimensional toy models for $G = SL(n, {\bf R})$, but we also discuss the 1 $+$ 1 dimensional model for $G = SL(2, {\bf R})$ which corresponds to the WZNW $\rightarrow$ Liouville reduction.

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