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Higher-rank supersymmetric models and topological conformal field theory. (English) Zbl 1245.81243
Summary: In the first part of this paper we investigate the operator aspect of a higher-rank supersymmetric model which is introduced as a Lie theoretic extension of the $N = 2$ minimal model with the simplest case $su(2)$ corresponding to the $N = 2$ minimal model. In particular we identify the analogs of chirality conditions and chiral ring. In the second part we construct a class of topological conformal field theories starting with this higher-rank supersymmetric model. We show the BRST-exactness of the twisted stress-energy tensor, find out physical observables and discuss how to make their correlation functions. It is emphasized that in the case of $su(2)$ the topological field theory constructed in this paper is distinct from the one obtained by twisting the $N = 2$ minimal model through the usual procedure.

81T40Two-dimensional field theories, conformal field theories, etc.
Full Text: DOI
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