Dimensional reduction by legendre transformation generates off-shell supersymmetric Yang-Mills theories

A new technique of dimensional reduction by Legendre transformation to derive off-shell formulations of extended supersymmetric theories is presented. The method starts from an on-shell theory in a higher dimension and retains a dependence of the fields upon one of the higher dimensions, thus allowing for a central charge in the four-dimensional supersymmetry algebra. The “hamiltonian density” of the theory plays the role of the lagrangian in one less dimension, while the equations of motion serve as constraints for the lower dimensional theory. These constraints guarantee supersymmetric and central charge invariances of the action. The technique is applied to derive off-shell formulations of the supersymmetric Yang-Mills theories.