On the SU(2|1) WZW model and its statistical mechanics applications

Abstract

Motivated by a careful analysis of the Laplacian on the supergroup $SU(2|1)$ we formulate a proposal for the state space of the $SU(2|1)$ WZNW model. We then use properties of $\widehat{sl}(2|1)$ characters to compute the partition function of the theory. In the special case of level $k=1$ the latter is found to agree with the properly regularized partition function for the continuum limit of the integrable $sl(2|1)3-\bar{3}$ super-spin chain. Some general conclusions applicable to other WZNW models (in particular the case $k=-1/2$) are also drawn.

38 pages, 2 figures

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