A systematic search for a realistic SU(n) tumbling gauge model

Within the framework of the dynamical symmetry breaking and the tumbling ideas, a systematic search was carried out in SU(n) groups with the ultimate aim of determining if a realistic and phenomenologically acceptable model exists which tumbles down to SU(3)_c ? U(1), or a suitable large group. To do so all the anomaly free and the asymptotically free fermion contents for any SU(n) were first determined. In order to have nontrivial tumbling the real and the pseudo-real representations have been eliminated, and the tumbling patterns of all the allowed complex ones in detail have been examined. No such realistic model has been found. These results combined with those of Srednicki's concerning the SO(4n + 2) and E₆ groups establish the fact that there cannot be any realistic tumbling gauge model within the context of the original tumbling hypotheses. Having thus established the need for a change of these hypotheses some suggestions and comment on various ways of remedying the problem are made.