n-Point Functions and Current Algebra

We show that two proposals for the incorporation of currents in dual n-point functions are very unlikely to be correct because of anomalies in their factorization or level-structure properties. The amplitude proposed by Bander has infinitely degenerate Regge trajectories even at the leading level. Amplitudes constructed according to a prescription by Sugawara and Ohba have a richer spectrum than that of hadronic n-point functions and, even worse, are internally inconsistent in their factorization properties. Finally we construct a set of dual functions for n external bosons, one vector current, and one scalar current which satisfy the Ward identities of a local vector-scalar current algebra. Only the scalar current has structure (pole-dominated) in these amplitudes. The vector current is structureless. Because of this simplification, the factorization inconsistency mentioned above does not apply, and it is very possible that a resonance-saturated current algebra which realizes essentially the Dashen-Gell-Mann program can be constructed from these amplitudes.