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Off-shell formulation of \(N=2\) nonlinear \(\sigma\)-models. (English) Zbl 1004.81564

Summary: We study \(d=2, N=(2,2)\) non-linear \(\sigma\)-models in \((2,2)\) superspace. By analyzing the most general constraints on a superfield, we show that through an appropriate choice of coordinates, there are no other superfields than chiral, twisted chiral and semi-chiral ones. We study the resulting \(\sigma\)-models and we speculate on the possibility that all \((2,2)\) non-linear \(\sigma\)-models can be described using these fields. We apply the results to two examples: the SU\((2)\times U(1)\) and the SU\((2)\times\text{SU}(2)\) WZW model. Pending upon the choice of complex structures, the former can be described in terms of either one semi-chiral multiplet or a chiral and a twisted chiral multiplet. The latter is formulated in terms of one semi-chiral and one twisted chiral multiplet. For both cases we obtain the potential explicitly.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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