We investigate the one-loop renormalisability of a general N = 1 2 supersymmetric gauge theory coupled to chiral matter, and show the existence of an N = 1 2 supersymmetric SU (N ) × U (1) theory which is renormalisable at one loop.

We construct a superpotential for the general N = 1 2 supersymmetric gauge theory coupled to chiral matter in the fundamental and adjoint representations, and investigate the one-loop renormalisability of the theories.

We show that the renormalisation of the N = 1 supersymmetric gauge theory when working in the component formalism, without eliminating auxiliary fields and using a standard covariant gauge, requires a non-linear renormalisation of the auxiliary fields.

We show that N = 1 2 supersymmetric gauge theory is renormalisable at one loop, but only after gauge invariance is restored in a non-trivial fashion.

No abstract