Supersymmetric gauge theories and their supercurrents

Using the method of dimensional reduction of N=l supersymmetric Yang-Mills theories from higher dimensions down to four dimensions, all possible supersymmetric Yang-Mills theories in four dimensions are obtained. The conserved currents associated with the symmetries of these models are then developed using Noether's theorem in ordinary space-time. By the variation of these conserved currents under supersymmetry transformations the supercurrent multiplets for the different models are obtained. Supersymmetric gauge theories are then discussed in superspace where differential geometry can be used to obtain Bianchi identities for the supersymmetric field strengths. The constraints on the field strengths that give rise to off-shell representations for each of the different supersymmetric gauge theories are then obtained and off-shell Lagrangians written down. The connection with supersymmetric gauge theories in ordinary space-time is made. The supercurrents in superspace are then derived using the generalization of Noether's theorem to superspace.