A transverse lattice model, with one lattice dimension and two continuum dimensions, is constructed by introducing Wess-Zumino terms into the gauged (1+1)-dimensional nonlinear sigma model action of the link fields. Its continuum limit is the pure Chern-Simons gauge theory in 2+1 dimensions. The lattice model is quantized, and some simple expectation values for Wilson loops on M 2 ×S 1 are evaluated. This construction provides an explicit connection between Chern-Simons theory and the gauged Wess-Zumino-Witten model.
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Paul A. Griffin (1992) studied this question.