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 sl ˆ ( 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.
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