Properties of Semi-Chiral Superfields

Whenever the N=(2,2) supersymmetry algebra of non-linear sigma-models in two dimensions does not close off-shell, a holomorphic two-form can be defined. The only known superfields providing candidate auxiliary fields to achieve an off-shell formulation are semi-chiral fields. Such a semi-chiral description is only possible when the two-form is constant. Using an explicit example, hyper-Kahler manifolds, we show that this is not always the case. Finally, we give a concrete construction of semi-chiral potentials for a class of hyper-Kahler manifolds using the duality exchanging a pair consisting of a chiral and a twisted-chiral superfield for one semi-chiral multiplet.