Anomaly-free complex representations in SU(N)

Abstract

We have found all irreducible, anomaly‐free and complex representations of SU(N) up to dimension 4×10⁹ and SU(16). None of these representations are asymptotically free. For each SU(N), we have given a complete list of complex reducible representations which satisfy both asymptotic and anomaly freedom. Applications of such solutions are briefly discussed.