Why auxiliary fields matter: the strange case of the 4D, N = 1 supersymmetric QCD effective action

Within a four dimensional manifestly N = 1 supersymmetric action, we show that Wess-Zumino-Novikov-Witten (WZNW) terms can be embedded in an extraordinarily simple manner into a purely chiral superaction. In order to achieve this result it is necessary to assign spin-0 and spin-12 degrees of freedom both to chiral superfields and as well to non-minimal scalar multiplets. We propose a new formulation for the effective low-energy action of 4D, N = 1 supersymmetric QCD that is consistent with holomorphy to all orders in the pion superfield. After reduction to a 2D, N = 2 theory we find a new class of manifestly supersymmetric non-linear σ-models with torsion.