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

TL;DR

This paper analyzes the $SU(2|1)$ WZW model, proposing a state space, computing its partition function, and connecting it to super-spin chain models, with implications for other WZNW models.

Contribution

It introduces a new formulation for the state space of the $SU(2|1)$ WZNW model and computes its partition function using superalgebra characters.

Findings

Partition function matches the continuum limit of an integrable super-spin chain at level 1.

Proposes a regularized partition function for the $SU(2|1)$ model.

Draws conclusions relevant to other WZNW models like $k=-1/2$.

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 $\hat{sl}(2|1)$ 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.