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

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 slˆ(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) 3-3¯ super-spin chain. Some general conclusions applicable to other WZNW models (in particular the case k=−1/2) are also drawn.