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 vertical bar 1) we formulate a proposal for the state space of the SU(2 vertical bar 1) WZNW model. We then use properties of (sl) over cap (2 vertical bar 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 vertical bar 1) 3-(3) over bar super-spin chain. Some general conclusions applicable to other WZNW models (in particular the case k = -1/2) are also drawn. (C) 2007 Elsevier B.V. All rights reserved.