Global symmetries in duals of supersymmetric SU(N)×SU(M) and application to composite axion

In this paper, we construct a supersymmetric composite axion (c-axion) model based on the gauge group SU(N)×SU(M), which is one possible physical application of the N=1 duality. The dual of SU(M) is interpreted as the color gauge group. We illustrate the existence of c-axion for the case of one dual quark in the dual gauge group SU(M̃).