On the \(\text{SU}(2| 1)\) WZNW model and its statistical mechanics applications. (English) Zbl 1119.82014
Summary: Motivated by a careful analysis of the Laplacian on the supergroup \(text{SU}(2|1)\) we formulate a proposal for the state space of the \(text{SU}(2|1)\) WZNW model. We then use properties of \(\widehat{\text{sl}}(2|1)\) 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 \(\text{sl}(2|1)_{3-\overline 3}\) super-spin chain. Some general conclusions applicable to other WZNW models (in particular the case \(k=-1/2)\) are also drawn.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 82B23 | Exactly solvable models; Bethe ansatz |
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