A FRESH LOOK AT GENERALIZED VENEZIANO AMPLITUDES

The dual resonance model, which was a precursor of string theory was b ased upon the idea that two-particle scattering amplitudes should be e xpressible equivalently as a sum of contributions of an infinite numbe r of s channel poles each corresponding to a finite number of particle s with definite spin, or as a similar sum of t channel poles. The famo us example of Veneziano [Nuovo Cimento A 57 (1968) 190] satisfies all these requirements, and is additionally ghost free. We recall other tr ajectories which provide solutions to the duality constraints, e.g. th e general Mobius trajectories and the logarithmic trajectories, which were thought to be lacking this last feature. We however demonstrate, partly empirically, the existence of a regime within a particular defo rmation of the Veneziano amplitude for logarithmic trajectories for wh ich the 4-point amplitude remains ghost free.