Alternative auxiliary fields for chiral multiplets

We study 3-form auxiliary field formulation for chiral multiplets in the Wess-Zumino model. The conventional auxiliary fields F and G are replaced by their Hodge duals K_μνρσ and H_μνρσ which are the field strengths of the 3-form potential auxiliary fields G_μνρ and F_μνρ. Even though duality transformations connect these two formulations, there exist certain differences from the conventional formulation. When boundary conditions are taken into account, the field equations in the 3-form formulation are equivalent to the conventional ones, while our Lagrangian is not. We also show that the new field strengths acquire generalized Chern-Simons terms. The O'Raifeartaigh mechanism works for spontaneous supersymmetry breaking also in the 3-form auxiliary field formulation via the boundary conditions on the 3-form auxiliary fields.