GAUGING SU(N-M)

We develop a local gauge theory of the graded algebra su( n m). We find the restrictions on the gauge potentials and matter fields in order that a physically suitable gauge invariant lagrangian exists. These conditions are: triviality of fields in extended dimensions, non-extended gauge components only lie in su(n) × su(m), and suitable restrictions satisfied by the extended gauge components. For matter the grading has to be given by chirality. © 1979.