O(n) relations for coupling constants and space-time dimensions in dual models

It is proposed that certain daughter trajectories arise as a consequence of a higher underlying O(n) symmetry, with n>3. This suggestion is motivated by the dual resonance model, where such a pattern arises naturally from the existence of a critical space-time dimension. This is easily confirmed in the model (and provides a simple test for what is the critical dimension) by considering the amplitudes for spinless particles. The results of pi N phase shift analysis are discussed to give a speculative phenomenological estimate of the appropriate higher symmetry. (16 refs).