SU(1,1) Analysis of Dual Resonance Models

The representations of the noncompact group SU(1,1) are discussed with regard to applications to dual resonance models. The Gliozzi operators are constructed from a standard differential representation of SU(1,1). We point out that the delicate limiting procedure appearing in the recent literature has its group-theoretical basis in the fact that SU(1,1), unlike its compact counterpart SU(2), has no nontrivial unitary spin-0 representation. We further note that the vertex appearing in the model effectively transforms as the spin-α₀ representation of the continuous class, exceptional interval, of SU(1,1). The N-point dual amplitude then appears as the coupling of N such vertices to the identity. Finally, we discuss the classification of the states in the model under the group. A complete classification in terms of SU(1,1) is shown to break down at α(s)=8 on and below the fourth daughter trajectory.