Off-shell formulation of N = 2 non-linear σ-models

Abstract We study d = 2, N = (2, 2) non-linear σ-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 σ-models and we speculate on the possibility that all (2, 2) non-linear σ-models can be described using these fields. We apply the results to two examples: the SU (2) × U(1) and the SU (2) × SU (2) WZW model. Pending upon the choice of complex structures, and 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.